Type: Package
Title: Boundary Adaptive Local Polynomial Conditional Density Estimator
Version: 0.1.6
Maintainer: Rajita Chandak <rajita.chandak@epfl.ch>
Description: Tools for estimation and inference of conditional densities, derivatives and functions. This is the companion software for Cattaneo, Chandak, Jansson and Ma (2024) <doi:10.3150/23-BEJ1711>.
Depends: R (≥ 3.3.0)
License: GPL (≥ 3)
Encoding: UTF-8
SystemRequirements: GNU make
RoxygenNote: 7.3.2
Imports: Rcpp (≥ 0.12.8), ggplot2, purrr, MASS, mvtnorm, combinat, Matrix, Rdpack, stats
RdMacros: Rdpack
LinkingTo: Rcpp, RcppArmadillo
Suggests: testthat (≥ 3.0.0), covr
Config/testthat/edition: 3
NeedsCompilation: yes
Packaged: 2025-02-25 13:31:33 UTC; rajitachandak
Author: Matias D. Cattaneo [aut], Michael Jansson [aut], Xinwei Ma [aut], Rajita Chandak [aut, cre]
Repository: CRAN
Date/Publication: 2025-02-25 14:30:02 UTC

S matrix Internal Function

Description

Generate Matrix

Usage

S_exact(lower = -1, upper = 1, eval_pt, p, kernel_type)

Arguments

eval_pt

evaluation point

p

Nonnegative integer, polynomial order.

kernel_type

String, kernel type

Value

a (p+1)-by-(p+1) matrix

Sx Matrix (Internal Function)

Description

S_x matrix.

Usage

S_x(x_data, q, kernel_type)

Arguments

x_data

Data of covariates.

q

Maximum degree for x.

kernel_type

Type of kernel function.

Value

S_x matrix

T_x matrix (Internal Function)

Description

Constructing the Tx matrix as described in the supplemental appendix.

Usage

T_x(x_data, eval_pt, q, h, kernel_type)

Arguments

x_data

Data of covariates.

eval_pt

Evaluation point.

q

Polynomial order for covariates.

h

Bandwidth.

kernel_type

Type of kernel function.

Value

Matrix.

T_y matrix (Internal Function)

Description

Constructing the Ty matrix as described in the supplemental appendix.

Usage

T_y(y_data, yp_data, p, kernel_type)

Arguments

y_data

Vector of data points.

p

Polynomial order.

kernel_type

Type of kernel function. Currently only works with uniform kernel.

Value

Matrix Ty.

T matrix Internal Function Generate Matrix

Description

T matrix Internal Function Generate Matrix

Usage

T_y_exact(lower = -1, upper = 1, eval_pt, p, kernel_type = "uniform")

Arguments

eval_pt

evaluation point

p

Nonnegative integer, polynomial order.

kernel_type

String, kernel type

Value

a (p+1)-by-(p+1) matrix

bx

Description

Function for estimating the constants in the estimation formula

Usage

b_x(datavec, s_mat, e_vec, q, kernel_type)

Arguments

datavec

Dataset, vector.

s_mat

S_hat matrix.

q

Polynomial order.

kernel_type

Kernel function choice.

Value

Vector of products for each data point.

Unit basis vector

Description

Function to generate unit basis vector according to polynomial order and derivative order. This function returns unit vector that is the same size as the vector returned by poly_base(x, p).

Usage

basis_vec(x, p, mu)

Arguments

x

Sample input scalar or vector.

p

Polynomial order.

mu

Derivative order.

Value

Vector of appropriate length with ones corresponding to entries of order mu.

Examples

basis_vec(x = 2, p = 5, mu = 1)

IROT Bandwidth selection

Description

Internal Function

Usage

bw_irot(y_data, x_data, y_grid, x, p, q, mu, nu, kernel_type, regularize)

Arguments

y_data

Numeric matrix/data frame, the raw data of independent.

x_data

Numeric matrix/data frame, the raw data of covariates.

y_grid

Numeric vector, the evaluation points.

x

Numeric, specifies the evaluation point(s) in the x-direction.

p

Integer, polynomial order.

q

Integer, polynomial order.

mu

Integer, order of derivative.

nu

Integer, order of derivative.

kernel_type

String, the kernel.

regularize

Boolean.

Value

bandwidth sequence

ROT Bandwidth selection

Description

Internal Function

Usage

bw_rot(y_data, x_data, y_grid, x, p, q, mu, nu, kernel_type, regularize)

Arguments

y_data

Numeric matrix/data frame, the raw data of independent.

x_data

Numeric matrix/data frame, the raw data of covariates.

y_grid

Numeric vector, the evaluation points.

x

Numeric, specifies the evaluation point(s) in the x-direction.

p

Integer, polynomial order.

q

Integer, polynomial order.

mu

Integer, order of derivative.

nu

Integer, order of derivative.

kernel_type

String, the kernel.

regularize

Boolean.

Value

bandwidth sequence

C matrix Internal Function

Description

C matrix Internal Function

Usage

c_exact(lower = -1, upper = -1, eval_pt, m, p, kernel_type)

Arguments

eval_pt

evaluation point.

m

derivative order.

p

Nonnegative integer, polynomial order.

kernel_type

String, kernel type

Value

a (p+1)-by-1 matrix

c_x vector (Internal Function)

Description

c_x vector generated as described in main paper.

Usage

c_x(x_data, eval_pt, m, q, h, kernel_type)

Arguments

x_data

Data of covariates.

eval_pt

Evaluation point.

m

Order of polynomial.

q

Maximum degree for x.

h

Bandwidth.

kernel_type

Type of kernel function.

Matrix invertibility check

Description

Function to check intertibility of matrix.

Usage

check_inv(m)

Arguments

m

Matrix

Value

TRUE if matrix is invertible.

Coef method for local polynomial density bandwidth selection

Description

The coef method for local polynomial density bandwidth selection objects.

Usage

## S3 method for class 'lpbwcde'
coef(object, ...)

Arguments

object

Class "lpbwcde" object, obtained by calling lpbwcde.

...

Other arguments.

Value

Matrix

A matrix containing y_grid points and selected bandwidths.

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Rajita Chandak (maintainer), Princeton University. rchandak@princeton.edu.

Michael Jansson, University of California Berkeley. mjansson@econ.berkeley.edu.

Xinwei Ma, University of California San Diego. x1ma@ucsd.edu.

See Also

lpbwcde for data-driven bandwidth selection.

Supported methods: coef.lpbwcde, print.lpbwcde, summary.lpbwcde.

n=100 x_data = as.matrix(rnorm(n, mean=0, sd=1)) y_data = as.matrix(rnorm(n, mean=0, sd=1)) y_grid = stats::quantile(y_data, seq(from=0.1, to=0.9, by=0.1))bandwidth selection

y_grid = stats::quantile(y_data, seq(from=0.1, to=0.9, by=0.1)) model2 = lpcde::lpbwcde(y_data=y_data, x_data=x_data, x=0, y_grid = y_grid, bw_type = "mse-rot") coef(model2)

Coef method for local polynomial density conditional estimation

Description

The coef method for local polynomial conditional density objects.

Usage

## S3 method for class 'lpcde'
coef(object, ...)

Arguments

object

Class "lpcde" object, obtained by calling lpcde.

...

Additional options.

Value

outputs

A matrix containing the estimates

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Rajita Chandak (maintainer), Princeton University. rchandak@princeton.edu

Michael Jansson, University of California Berkeley. mjansson@econ.berkeley.edu.

Xinwei Ma, University of California San Diego. x1ma@ucsd.edu.

See Also

lpcde for local polynomial conditional density estimation.

Supported methods: coef.lpcde, confint.lpcde, plot.lpcde, print.lpcde, summary.lpcde, vcov.lpcde

Examples

n <- 100
x_data <- as.matrix(rnorm(n, mean = 0, sd = 1))
y_data <- as.matrix(rnorm(n, mean = 0, sd = 1))
y_grid <- stats::quantile(y_data, seq(from = 0.1, to = 0.9, by = 0.1))
# density estimation
model1 <- lpcde::lpcde(x_data = x_data, y_data = y_data, y_grid = y_grid, x = 0, bw = 0.5)
coef(model1)

Confint method for local polynomial density conditional estimation

Description

The confint method for local polynomial conditional density objects.

Usage

## S3 method for class 'lpcde'
confint(
  object,
  parm = NULL,
  level = 0.95,
  CIuniform = FALSE,
  CIsimul = 2000,
  ...
)

Arguments

object

Class "lpdensity" object, obtained by calling lpcde.

parm

Integer, indicating which parameters are to be given confidence intervals.

level

Numeric scalar between 0 and 1, the confidence level for computing confidence intervals/bands. Equivalent to (1-significance level).

CIuniform

TRUE or FALSE (default), plotting either pointwise confidence intervals (FALSE) or uniform confidence bands (TRUE).

CIsimul

Positive integer, specifies the number of simulations used to construct critical values (default is 2000). This option is ignored if CIuniform=FALSE.

...

Additional options, including (i) grid specifies a subset of grid points to display the bandwidth; (ii) gridIndex specifies the indices of grid points to display the bandwidth (this is the same as parm);(iii) CIuniform specifies whether displaying pointwise confidence intervals (FALSE, default) or the uniform confidence band (TRUE); (iv) CIsimul specifies the number of simulations used to construct critical values (default is 2000).

Value

Estimate

A matrix containing grid points, estimates and confidence interval end points using p- and q-th order local polynomials as well as bias-corrected estimates and corresponding confidence intervals.

crit_val

The critical value used in computing the confidence interval end points.

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Rajita Chandak (maintainer), Princeton University. rchandak@princeton.edu.

Michael Jansson, University of California Berkeley. mjansson@econ.berkeley.edu.

Xinwei Ma, University of California San Diego. x1ma@ucsd.edu.

See Also

lpcde for local polynomial conditional density estimation.

Supported methods: coef.lpcde, confint.lpcde, plot.lpcde, print.lpcde, summary.lpcde, vcov.lpcde

Examples

n <- 100
x_data <- as.matrix(rnorm(n, mean = 0, sd = 1))
y_data <- as.matrix(rnorm(n, mean = 0, sd = 1))
y_grid <- stats::quantile(y_data, seq(from = 0.1, to = 0.9, by = 0.1))
# density estimation
model1 <- lpcde::lpcde(x_data = x_data, y_data = y_data, y_grid = y_grid, x = 0, bw = 0.5)
confint(model1)

cov_hat: covariance estimator

Description

Function for estimating the variance-covariance matrix.

Usage

cov_hat(x_data, y_data, x, y_grid, p, q, mu, nu, h, kernel_type, cov_flag)

Arguments

x_data

Covariate dataset, vector or matrix.

y_data

Response variable dataset, vector.

x

Numeric vector or matrix, specifies the grid of evaluation points along x-direction.

y_grid

Numeric vector, specifies the grid of evaluation points along y-direction.

p

Polynomial order for y.

q

Polynomial order for covariates.

mu

Degree of derivative with respect to y.

nu

Degree of derivative with respect to x.

h

Numeric, bandwidth vector.

kernel_type

Kernel function choice.

cov_flag

Flag for covariance estimation option.

Value

Covariance matrix for all the grid points

Estimator construction

Description

Function for estimating the density function and its derivatives.

Usage

fhat(x_data, y_data, x, y_grid, p, q, mu, nu, h, kernel_type)

Arguments

x_data

Covariate dataset, vector or matrix.

y_data

Response variable dataset, vector.

x

Numeric vector or matrix, specifies the grid of evaluation points along x-direction.

y_grid

Numeric vector, specifies the grid of evaluation points along y-direction.

p

Polynomial order for y.

q

Polynomial order for covariates.

mu

Degree of derivative with respect to y.

nu

Degree of derivative with respect to x.

h

Numeric, bandwidth vector.

kernel_type

Kernel function choice.

Value

Conditional density estimate at all grid points.

Lp integral (Internal Function)

Description

Local polynomial integral evaluation calculation of elements of S_y and middle integral (evaluating integral at end points).

Usage

int_val(l, a, b, kernel_type)

Arguments

l

Degree of polynomial being integrated.

a

Lower limit of integration.

b

Upper limit of integration.

kernel_type

Type of kernel function. Choose from "uniform", "triangular", "epanechnikov".

Value

Value of integral.

Kernel Evaluation function (Internal Function)

Description

Function that evaluates product kernel at x based on the chosen function.

Usage

kernel_eval(x, kernel_type)

Arguments

x

Evaluation point.

kernel_type

Type of kernel function. Choose from "uniform", "triangular", "epanechnikov".

Value

Kernel evaluated at x.

Data-driven bandwidth selection for local polynomial conditional density estimators

Description

lpbwcde implements the bandwidth selection methods for local polynomial based conditional density (and derivatives) estimation proposed and studied in (Cattaneo et al. 2024).

Companion command: lpcde for estimation and robust bias-corrected inference.

Related Stata and R packages useful for nonparametric estimation and inference are available at https://nppackages.github.io/.

Usage

lpbwcde(
  y_data,
  x_data,
  x,
  y_grid = NULL,
  p = NULL,
  q = NULL,
  grid_spacing = "",
  ng = NULL,
  mu = NULL,
  nu = NULL,
  kernel_type = c("epanechnikov", "triangular", "uniform"),
  bw_type = c("imse-rot", "mse-rot"),
  regularize = NULL
)

Arguments

y_data

Numeric matrix/data frame, the raw data of independent.

x_data

Numeric matrix/data frame, the raw data of covariates.

x

Numeric, specifies the evaluation point in the x-direction. Default is median of the dataset.

y_grid

Numeric, specifies the grid of evaluation points. When set to default, grid points will be chosen as 0.05-0.95 percentiles of the data, with a step size of 0.05.

p

Nonnegative integer, specifies the order of the local polynomial for Y used to construct point estimates. (Default is 2.)

q

Nonnegative integer, specifies the order of the local polynomial for X used to construct point estimates. (Default is 1.)

grid_spacing

String, If equal to "quantile" will generate quantile-spaced grid evaluation points, otherwise will generate equally spaced points.

ng

Int, number of grid points to be used in generating bandwidth estimates.

mu

Nonnegative integer, specifies the derivative with respect to Y of the distribution function to be estimated. 0 for the distribution function, 1 (default) for the density funtion, etc.

nu

Nonnegative integer, specifies the derivative with respect to X of the distribution function to be estimated.

kernel_type

String, specifies the kernel function, should be one of "triangular", "uniform" or "epanechnikov".

bw_type

String, specifies the method for data-driven bandwidth selection. This option will be ignored if bw is provided. Implementable with "mse-rot" (default, mean squared error-optimal bandwidth selected for each grid point)

regularize

Boolean (default TRUE). Option to regularize bandwidth selection to have atleast 20+max(p, q)+1 datapoints when evaluating the estimator.

Value

BW

A matrix containing (1) y_grid (grid point), (2) bw (bandwidth)

opt

A list containing options passed to the function.

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Rajita Chandak (maintainer), Princeton University. rchandak@princeton.edu.

Michael Jansson, University of California Berkeley. mjansson@econ.berkeley.edu.

Xinwei Ma, University of California San Diego. x1ma@ucsd.edu.

References

Cattaneo MD, Chandak R, Jansson M, Ma X (2024). “Local Polynomial Conditional Density Estimators.” Bernoulli, 30(4), 3193-3223.

See Also

Supported methods: coef.lpbwcde, print.lpbwcde, summary.lpbwcde.

Examples

# Generate a random sample
set.seed(42)
x_data <- rnorm(2000)
y_data <- rnorm(2000, mean = x_data)
x <- 0

# Construct bandwidth
bw1 <- lpbwcde(y_data = y_data, x_data = x_data, x = x, bw_type = "mse-rot")
summary(bw1)

# Display bandwidths for a subset of y_grid points
summary(bw1, y_grid = bw1$BW[2:5, "y_grid"])

Local polynomial conditional density estimation

Description

lpcde implements the local polynomial regression based conditional density (and derivatives). The estimator proposed in (Cattaneo et al. 2024). Robust bias-corrected inference methods, both pointwise (confidence intervals) and uniform (confidence bands), are also implemented.

Usage

lpcde(
  x_data,
  y_data,
  y_grid = NULL,
  x = NULL,
  bw = NULL,
  p = NULL,
  q = NULL,
  p_RBC = NULL,
  q_RBC = NULL,
  mu = NULL,
  nu = NULL,
  rbc = TRUE,
  ng = NULL,
  cov_flag = c("full", "diag", "off"),
  normalize = FALSE,
  nonneg = FALSE,
  grid_spacing = "",
  kernel_type = c("epanechnikov", "triangular", "uniform"),
  bw_type = NULL
)

Arguments

x_data

Numeric matrix/data frame, the raw data of covariates.

y_data

Numeric matrix/data frame, the raw data of independent.

y_grid

Numeric, specifies the grid of evaluation points in the y-direction. When set to default, grid points will be chosen as 0.05-0.95 percentiles of the data, with a step size of 0.05 in y-direction.

x

Numeric, specifies the grid of evaluation points in the x-direction. When set to default, the evaluation point will be chosen as the median of the x data. To generate estimates for multiple conditioning values, please loop over the x values and evaluate the lpcde function at each point.

bw

Numeric, specifies the bandwidth used for estimation. Can be (1) a positive scalar (common bandwidth for all grid points); or (2) a positive numeric vector/matrix specifying bandwidths for each grid point (should be the same dimension as grid).

p

Nonnegative integer, specifies the order of the local polynomial for Y used to construct point estimates. (Default is 2.)

q

Nonnegative integer, specifies the order of the local polynomial for X used to construct point estimates. (Default is 1.)

p_RBC

Nonnegative integer, specifies the order of the local polynomial for Y used to construct bias-corrected point estimates. (Default is p+1.)

q_RBC

Nonnegative integer, specifies the order of the local polynomial for X used to construct bias-corrected point estimates. (Default is q+1.)

mu

Nonnegative integer, specifies the derivative with respect to Y of the distribution function to be estimated. 0 for the distribution function, 1 (default) for the density funtion, etc.

nu

Nonnegative integer, specifies the derivative with respect to X of the distribution function to be estimated. Default value is 0.

rbc

Boolean. TRUE (default) for rbc calcuations, required for valid uniform inference.

ng

Int, number of grid points to be used. generates evenly space points over the support of the data.

cov_flag

String, specifies covariance computation. Must be one of "full" (default), "diag" or "off".

normalize

Boolean, False (default) returns original estimator, True normalizes estimates to integrate to 1.

nonneg

Boolean, False (default) returns original estimator, True returns maximum of estimate and 0.

grid_spacing

String, If equal to "quantile" will generate quantile-spaced grid evaluation points, otherwise will generate equally spaced points.

kernel_type

String, specifies the kernel function, should be one of "triangular", "uniform", and "epanechnikov"(default).

bw_type

String, specifies the method for data-driven bandwidth selection. This option will be ignored if bw is provided. Implementable with "mse-dpi" (default, mean squared error-optimal bandwidth selected for each grid point)

Details

Bias correction is only used for the construction of confidence intervals/bands, but not for point estimation. The point estimates, denoted by est, are constructed using local polynomial estimates of order p and q, while the centering of the confidence intervals/bands, denoted by est_RBC, are constructed using local polynomial estimates of order p_RBC and q_RBC. The confidence intervals/bands take the form: [est_RBC - cv * SE(est_RBC) , est_RBC + cv * SE(est_RBC)], where cv denotes the appropriate critical value and SE(est_RBC) denotes an standard error estimate for the centering of the confidence interval/band. As a result, the confidence intervals/bands may not be centered at the point estimates because they have been bias-corrected. Setting p_RBC equal to p and q_RBC to q, results on centered at the point estimate confidence intervals/bands, but requires undersmoothing for valid inference (i.e., (I)MSE-optimal bandwdith for the density point estimator cannot be used). Hence the bandwidth would need to be specified manually when q=p, and the point estimates will not be (I)MSE optimal. See Cattaneo, Jansson and Ma (2020a, 2020b) for details, and also Calonico, Cattaneo, and Farrell (2018, 2020) for robust bias correction methods.

Sometimes the density point estimates may lie outside of the confidence intervals/bands, which can happen if the underlying distribution exhibits high curvature at some evaluation point(s). One possible solution in this case is to increase the polynomial order p or to employ a smaller bandwidth.

Value

Estimate

A matrix containing (1) grid (grid points),
(2) bw (bandwidths),
(3) est (point estimates with p-th and q-th order local polynomial),
(4) est_RBC (point estimates with p_RBC-th and q_RBC-th order local polynomial),
(5) se (standard error corresponding to est. Set to NA if cov_flag="off"). (6) se_RBC (standard error corresponding to est_RBC). Set to NA if cov_flag="off"

CovMat

The variance-covariance matrix corresponding to est. Will be 0 if cov_flag="off" or a diagonal matrix if cov_flag="diag".

opt

A list containing options passed to the function.

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Rajita Chandak (maintainer), Princeton University. rchandak@princeton.edu.

Michael Jansson, University of California Berkeley. mjansson@econ.berkeley.edu.

Xinwei Ma, University of California San Diego. x1ma@ucsd.edu.

References

Cattaneo MD, Chandak R, Jansson M, Ma X (2024). “Local Polynomial Conditional Density Estimators.” Bernoulli, 30(4), 3193-3223.
Calonico S, Cattaneo MD, Farrell MH (2018). “On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference.” Journal of the American Statistical Association, 113(522), 767–779.
Calonico S, Cattaneo MD, Farrell MH (2022). “Coverage Error Optimal Confidence Intervals for Local Polynomial Regression.” Bernoulli, 28(4), 2998–3022.
Cattaneo MD, Jansson M, Ma X (2020). “Simple local polynomial density estimators.” J. Amer. Statist. Assoc., 115(531), 1449–1455.

See Also

Supported methods: coef.lpcde, confint.lpcde, plot.lpcde, print.lpcde, summary.lpcde, vcov.lpcde

Examples

# Density estimation example
n <- 500
x_data <- matrix(rnorm(n, mean = 0, sd = 1))
y_data <- matrix(rnorm(n, mean = x_data, sd = 1))
y_grid <- seq(from = -1, to = 1, length.out = 5)
model1 <- lpcde::lpcde(x_data = x_data, y_data = y_data, y_grid = y_grid, x = 0, bw = 0.5)
# summary of estimation
summary(model1)

lpcde_fn: Conditional density estimator.

Description

Function for estimating the density function and its derivatives.

Usage

lpcde_fn(
  y_data,
  x_data,
  y_grid,
  x,
  p,
  q,
  p_RBC,
  q_RBC,
  bw,
  mu,
  nu,
  cov_flag,
  kernel_type,
  rbc = FALSE
)

Arguments

y_data

Response variable dataset, vector.

x_data

Covariate dataset, vector or matrix.

y_grid

Numeric vector, specifies the grid of evaluation points along y-direction.

x

Numeric vector or matrix, specifies the grid of evaluation points along x-direction.

p

Polynomial order for y.

q

Polynomial order for covariates.

p_RBC

Nonnegative integer, specifies the order of the local polynomial for Y used to construct bias-corrected point estimates. (Default is p+1.)

q_RBC

Nonnegative integer, specifies the order of the local polynomial for X used to construct bias-corrected point estimates. (Default is q+1.)

bw

Numeric, bandwidth vector.

mu

Degree of derivative with respect to y.

nu

Degree of derivative with respect to x.

cov_flag

Flag for covariance estimation option.

kernel_type

Kernel function choice.

rbc

Boolean for whether to return RBC estimate and standard errors.

Value

Conditional density estimate at all grid points.

Polynomial order vector

Description

Generates list of all combinations of length less than or equal to d of numbers that add up to n.

Usage

mvec(n, d)

Arguments

n

Total value of each combination

d

Maximum length of combinations

Internal function.

Description

Calculates density and higher order derivatives for Gaussian models.

Usage

normal_dgps(x, v, mean, sd)

Arguments

x

Scalar, point of evaluation.

v

Nonnegative integer, the derivative order (0 indicates cdf, 1 indicates pdf, etc.).

mean

Scalar, the mean of the normal distribution.

sd

Strictly positive scalar, the standard deviation of the normal distribution.

Plot method for local polynomial density conditional estimation

Description

The plot method for local polynomial density objects. A standard ggplot2 object is returned, hence can be used for further customization.

Usage

## S3 method for class 'lpcde'
plot(
  ...,
  alpha = NULL,
  type = NULL,
  lty = NULL,
  lwd = NULL,
  lcol = NULL,
  pty = NULL,
  pwd = NULL,
  pcol = NULL,
  y_grid = NULL,
  CItype = NULL,
  CIuniform = FALSE,
  CIsimul = 2000,
  CIshade = NULL,
  CIcol = NULL,
  title = NULL,
  xlabel = NULL,
  ylabel = NULL,
  legendTitle = NULL,
  legendGroups = NULL,
  rbc = FALSE
)

Arguments

...

Class "lpcde" object, obtained from calling lpcde.

alpha

Numeric scalar between 0 and 1, specifies the significance level for plotting confidence intervals/bands.

type

String, one of "line" (default), "points" and "both", specifies how the point estimates are plotted. If more than one is provided, they will be applied to each data series accordingly.

lty

Line type for point estimates, only effective if type is "line" or "both". 1 for solid line, 2 for dashed line, 3 for dotted line. For other options, see the instructions for ggplot2 . If more than one is provided, they will be applied to each data series accordingly.

lwd

Line width for point estimates, only effective if type is "line" or "both". Should be strictly positive. For other options, see the instructions for ggplot2 . If more than one is provided, they will be applied to each data series accordingly.

lcol

Line color for point estimates, only effective if type is "line" or "both". 1 for black, 2 for red, 3 for green, 4 for blue. For other options, see the instructions for ggplot2 . If more than one is provided, they will be applied to each data series accordingly.

pty

Scatter plot type for point estimates, only effective if type is "points" or "both". For options, see the instructions for ggplot2 . If more than one is provided, they will be applied to each data series accordingly.

pwd

Scatter plot size for point estimates, only effective if type is "points" or "both". Should be strictly positive. If more than one is provided, they will be applied to each data series accordingly.

pcol

Scatter plot color for point estimates, only effective if type is "points" or "both". 1 for black, 2 for red, 3 for green, 4 for blue. For other options, see the instructions for ggplot2 . If more than one is provided, they will be applied to each data series accordingly.

y_grid

Numeric vector, specifies a subset of grid points to plot point estimates. This option is effective only if type is "points" or "both"; or if CItype is "ebar" or "all".

CItype

String, one of "region" (shaded region, default), "line" (dashed lines), "ebar" (error bars), "all" (all of the previous) or "none" (no confidence region), how the confidence region should be plotted. If more than one is provided, they will be applied to each data series accordingly.

CIuniform

TRUE or FALSE (default), plotting either pointwise confidence intervals (FALSE) or uniform confidence bands (TRUE).

CIsimul

Positive integer, specifies the number of simulations used to construct critical values (default is 2000). This option is ignored if CIuniform=FALSE.

CIshade

Numeric, specifies the opaqueness of the confidence region, should be between 0 (transparent) and

  1. Default is 0.2. If more than one is provided, they will be applied to each data series accordingly.

CIcol

Color of the confidence region. 1 for black, 2 for red, 3 for green, 4 for blue. For other options, see the instructions for ggplot2 . If more than one is provided, they will be applied to each data series accordingly.

title, xlabel, ylabel

Strings, specifies the title of the plot and labels for the x- and y-axis.

legendTitle

String, specifies the legend title.

legendGroups

String vector, specifies the group names used in legend.

rbc

TRUE or FALSE (default), plotting confidence intervals and bands with standard estimates (FALSE) or RBC estimates (TRUE).

Value

Figure

A standard ggplot2 object is returned, hence can be used for further customization.

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Rajita Chandak (maintainer), Princeton University. rchandak@princeton.edu

Michael Jansson, University of California Berkeley. mjansson@econ.berkeley.edu.

Xinwei Ma, University of California San Diego. x1ma@ucsd.edu.

See Also

lpcde for local polynomial density estimation. Supported methods: coef.lpcde, confint.lpcde, plot.lpcde, print.lpcde, summary.lpcde, vcov.lpcde

Polynomial basis vector expansion

Description

Generate polynomial basis vector up to order p. has multivariate functionality as described in the main paper normalized by factorials in denominator. NOTE: currently works only up to 4th degree polynomial expansion for multivariate x.

Usage

poly_base(x, p)

Arguments

x

A number or vector.

p

A number (integer).

Value

Polynomial basis of x up to degree p.

Examples

poly_base(x = 2, p = 5)

Print method for local polynomial conditional density bandwidth selection

Description

The print method for local polynomial conditional density bandwidth selection objects.

Usage

## S3 method for class 'lpbwcde'
print(x, ...)

Arguments

x

Class "lpbwcde" object, obtained by calling lpbwcde.

...

Other arguments.

Value

Display output

A list of specified options provided to the function.

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Rajita Chandak (maintainer), Princeton University. rchandak@princeton.edu.

Michael Jansson, University of California Berkeley. mjansson@econ.berkeley.edu.

Xinwei Ma, University of California San Diego. x1ma@ucsd.edu.

See Also

lpbwcde for data-driven bandwidth selection.

Supported methods: coef.lpbwcde, print.lpbwcde, summary.lpbwcde.

Examples

n <- 100
x_data <- as.matrix(rnorm(n, mean = 0, sd = 1))
y_data <- as.matrix(rnorm(n, mean = 0, sd = 1))
y_grid <- stats::quantile(y_data, seq(from = 0.1, to = 0.9, by = 0.1))
# bandwidth selection
y_grid <- stats::quantile(y_data, seq(from = 0.1, to = 0.9, by = 0.1))
model2 <- lpcde::lpbwcde(y_data = y_data, x_data = x_data, x = 0,
                         y_grid = y_grid, bw_type = "mse-rot")
print(model2)

Print method for local polynomial conditional density estimation

Description

The print method for local polynomial conditional density objects.

Usage

## S3 method for class 'lpcde'
print(x, ...)

Arguments

x

Class "lpcde" object, obtained from calling lpcde.

...

Additional options.

Value

Display output

summary of inputs to lpcde

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Rajita Chandak (maintainer), Princeton University. rchandak@princeton.edu.

Michael Jansson, University of California Berkeley. mjansson@econ.berkeley.edu.

Xinwei Ma, University of California San Diego. x1ma@ucsd.edu.

See Also

lpcde for local polynomial conditional density estimation. Supported methods: coef.lpcde, confint.lpcde, plot.lpcde, print.lpcde, summary.lpcde, vcov.lpcde

Examples

n <- 100
x_data <- as.matrix(rnorm(n, mean = 0, sd = 1))
y_data <- as.matrix(rnorm(n, mean = 0, sd = 1))
y_grid <- stats::quantile(y_data, seq(from = 0.1, to = 0.9, by = 0.1))
# density estimation
model1 <- lpcde::lpcde(x_data = x_data, y_data = y_data, y_grid = y_grid, x = 0, bw = 0.5)
print(model1)

Description

Function that prints all combinations of natural numbers that add up to target value.

Usage

print_all_sumC(target)

Arguments

target

Target value for sum.

Value

List of combinations that add up to target value.

Summary method for local polynomial conditional density bandwidth selection

Description

The summary method for local polynomial conditional density bandwidth selection objects.

Usage

## S3 method for class 'lpbwcde'
summary(object, ...)

Arguments

object

Class "lpbwcde" object, obtained by calling lpbwcde.

...

Additional options, including (i) y_grid specifies a subset of y_grid points to display the bandwidth; (ii) gridIndex specifies the indices of y_grid points to display the bandwidth.

Value

Display output

A list of specified options and a matrix of grid points, bandwidth, and effective sample size.

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Rajita Chandak (maintainer), Princeton University. rchandak@princeton.edu.

Michael Jansson, University of California Berkeley. mjansson@econ.berkeley.edu.

Xinwei Ma, University of California San Diego. x1ma@ucsd.edu.

See Also

lpbwcde for data-driven bandwidth selection.

Supported methods: coef.lpbwcde, print.lpbwcde, summary.lpbwcde.

Examples

n <- 100
x_data <- as.matrix(rnorm(n, mean = 0, sd = 1))
y_data <- as.matrix(rnorm(n, mean = 0, sd = 1))
y_grid <- stats::quantile(y_data, seq(from = 0.1, to = 0.9, by = 0.1))
# bandwidth selection
y_grid <- stats::quantile(y_data, seq(from = 0.1, to = 0.9, by = 0.1))
model2 <- lpcde::lpbwcde(y_data = y_data, x_data = x_data, x = 0,
                         y_grid = y_grid, bw_type = "mse-rot")
summary(model2)

Summary method for local polynomial density conditional estimation

Description

The summary method for local polynomial conditional density objects.

Usage

## S3 method for class 'lpcde'
summary(object, ...)

Arguments

object

Class "lpcde" object, obtained from calling lpcde.

...

Additional options, including (i)y_grid specifies a subset of grid points in y- directions to display results; (ii) gridIndex specifies the indices of grid points to display results; (iii) alpha specifies the significance level; (iv) CIuniform specifies whether displaying pointwise confidence intervals (FALSE, default) or the uniform confidence band (TRUE); (v) CIsimul specifies the number of simulations used to construct critical values (default is 2000).

Value

Display output

A list of specified options and a matrix of grid points and estimates.

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Rajita Chandak (maintainer), Princeton University. rchandak@princeton.edu

Michael Jansson, University of California Berkeley. mjansson@econ.berkeley.edu.

Xinwei Ma, University of California San Diego. x1ma@ucsd.edu.

See Also

lpcde for local polynomial conditional density estimation. Supported methods: coef.lpcde, confint.lpcde, plot.lpcde, print.lpcde, summary.lpcde, vcov.lpcde

Examples

n <- 100
x_data <- as.matrix(rnorm(n, mean = 0, sd = 1))
y_data <- as.matrix(rnorm(n, mean = 0, sd = 1))
y_grid <- stats::quantile(y_data, seq(from = 0.1, to = 0.9, by = 0.1))
# density estimation
model1 <- lpcde::lpcde(x_data = x_data, y_data = y_data, y_grid = y_grid, x = 0, bw = 0.5)
summary(model1)

Variance-Covariance

Description

The vcov method for local polynomial conditional density objects.

Usage

## S3 method for class 'lpcde'
vcov(object, ...)

Arguments

object

Class "lpdensity" object, obtained by calling lpcde.

...

Additional options.

Details

Vcov method for local polynomial density conditional estimation

Value

stdErr

A matrix containing grid points and standard errors using p- and q-th order local polynomials.

CovMat

The variance-covariance matrix corresponding to est.

CovMat_RBC

The variance-covariance matrix corresponding to est_RBC.

Author(s)

Matias D. Cattaneo, Princeton University. cattaneo@princeton.edu.

Rajita Chandak (maintainer), Princeton University. rchandak@princeton.edu.

Michael Jansson, University of California Berkeley. mjansson@econ.berkeley.edu.

Xinwei Ma, University of California San Diego. x1ma@ucsd.edu.

See Also

lpcde for local polynomial conditional density estimation.

Supported methods: plot.lpcde, print.lpcde, summary.lpcde,

Examples

n <- 100
x_data <- as.matrix(rnorm(n, mean = 0, sd = 1))
y_data <- as.matrix(rnorm(n, mean = 0, sd = 1))
y_grid <- stats::quantile(y_data, seq(from = 0.1, to = 0.9, by = 0.1))
# density estimation
model1 <- lpcde::lpcde(x_data = x_data, y_data = y_data, y_grid = y_grid, x = 0, bw = 0.5)
vcov(model1)