Title:	Flexible Inference via Permutations in R
Version:	0.3.3
Description:	A flexible permutation framework for making inference such as point estimation, confidence intervals or hypothesis testing, on any kind of data, be it univariate, multivariate, or more complex such as network-valued data, topological data, functional data or density-valued data.
License:	GPL (≥ 3)
Encoding:	UTF-8
RoxygenNote:	7.2.3
Imports:	cli, dials, ggplot2, magrittr, optimParallel, pbapply, purrr, R6, Rcpp, rgenoud, rlang, tibble, usethis, viridisLite, withr
Suggests:	covr, dplyr, htmltools, htmlwidgets, interp, knitr, plotly, rmarkdown, testthat (≥ 3.0.0), tidyr
VignetteBuilder:	knitr
URL:	https://LMJL-Alea.github.io/flipr/, https://github.com/LMJL-Alea/flipr/
BugReports:	https://github.com/LMJL-Alea/flipr/issues/
Depends:	R (≥ 2.10)
LinkingTo:	Rcpp
Config/testthat/edition:	3
NeedsCompilation:	yes
Packaged:	2023-08-22 08:34:24 UTC; stamm-a
Author:	Alessia Pini [aut], Aymeric Stamm [aut, cre], Simone Vantini [aut], Juliette Chiapello [ctb]
Maintainer:	Aymeric Stamm <aymeric.stamm@cnrs.fr>
Repository:	CRAN
Date/Publication:	2023-08-23 09:00:02 UTC

flipr: Flexible inference via permutations in R

Description

The flipr package provides a flexible permutation framework for making inference such as point estimation, confidence intervals or hypothesis testing, on any kind of data, be it univariate, multivariate, or more complex such as network-valued data, topological data, functional data or density-valued data.

Author(s)

Maintainer: Aymeric Stamm aymeric.stamm@cnrs.fr (ORCID)

Authors:

• Alessia Pini alessia.pini@unicatt.it

• Simone Vantini simone.vantini@polimi.it

Other contributors:

• Juliette Chiapello [contributor]

See Also

Useful links:

• https://LMJL-Alea.github.io/flipr/

• https://github.com/LMJL-Alea/flipr/

• Report bugs at https://github.com/LMJL-Alea/flipr/issues/

Pipe operator

Description

See magrittr::%>% for details.

Usage

lhs %>% rhs

R6 Class representing a plausibility function

Description

A plausibility function is...

Public fields

Methods

Public methods

• PlausibilityFunction$new()

• PlausibilityFunction$set_nperms()

• PlausibilityFunction$set_nperms_max()

• PlausibilityFunction$set_alternative()

• PlausibilityFunction$set_aggregator()

• PlausibilityFunction$set_pvalue_formula()

• PlausibilityFunction$get_value()

• PlausibilityFunction$set_max_conf_level()

• PlausibilityFunction$set_point_estimate()

• PlausibilityFunction$set_parameter_bounds()

• PlausibilityFunction$set_grid()

• PlausibilityFunction$evaluate_grid()

• PlausibilityFunction$clone()

Method new()

Create a new plausibility function object.

Usage

PlausibilityFunction$new(
  null_spec,
  stat_functions,
  stat_assignments,
  ...,
  seed = NULL
)

Arguments

Returns

A new PlausibilityFunction object.

Method set_nperms()

Change the value of the nperms field.

Usage

PlausibilityFunction$set_nperms(val)

Arguments

Examples

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {purrr::map(y, ~ .x - parameters[1])}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$nperms
pf$set_nperms(10000)
pf$nperms

Method set_nperms_max()

Change the value of the nperms_max field.

Usage

PlausibilityFunction$set_nperms_max(val)

Arguments

Examples

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {purrr::map(y, ~ .x - parameters[1])}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$nperms_max
pf$set_nperms_max(10000)
pf$nperms_max

Method set_alternative()

Change the value of the alternative field.

Usage

PlausibilityFunction$set_alternative(val)

Arguments

Examples

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {purrr::map(y, ~ .x - parameters[1])}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$alternative
pf$set_alternative("right_tail")
pf$alternative

Method set_aggregator()

Change the value of the aggregator field.

Usage

PlausibilityFunction$set_aggregator(val)

Arguments

Examples

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {purrr::map(y, ~ .x - parameters[1])}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$aggregator
pf$set_aggregator("fisher")
pf$aggregator

Method set_pvalue_formula()

Change the value of the pvalue_formula field.

Usage

PlausibilityFunction$set_pvalue_formula(val)

Arguments

Examples

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {
  purrr::map(y, ~ .x - parameters[1])
}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$pvalue_formula
pf$set_pvalue_formula("estimate")
pf$pvalue_formula

Method get_value()

Computes an indicator of the plausibility of specific values for the parameters of interest in the form of a p-value of an hypothesis test against these values.

Usage

PlausibilityFunction$get_value(
  parameters,
  keep_null_distribution = FALSE,
  keep_permutations = FALSE,
  ...
)

Arguments

Examples

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {purrr::map(y, ~ .x - parameters[1])}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$set_nperms(50)
pf$get_value(2)

Method set_max_conf_level()

Change the value of the max_conf_level field.

Usage

PlausibilityFunction$set_max_conf_level(val)

Arguments

Examples

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {
  purrr::map(y, ~ .x - parameters[1])
}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$max_conf_level
pf$set_max_conf_level(0.999)
pf$max_conf_level

Method set_point_estimate()

Change the value of the point_estimate field.

Usage

PlausibilityFunction$set_point_estimate(
  point_estimate = NULL,
  lower_bound = -10,
  upper_bound = 10,
  ncores = 1L,
  estimate = FALSE,
  overwrite = FALSE
)

Arguments

Examples

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {
  purrr::map(y, ~ .x - parameters[1])
}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$point_estimate
pf$set_point_estimate(mean(y) - mean(x))
pf$point_estimate

Method set_parameter_bounds()

Change the value of the parameters field.

Updates the range of the parameters under investigation.

Usage

PlausibilityFunction$set_parameter_bounds(point_estimate, conf_level)

Arguments

Examples

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {
  purrr::map(y, ~ .x - parameters[1])
}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$set_nperms(50)
pf$set_point_estimate(point_estimate = mean(y) - mean(x))
pf$parameters
pf$set_parameter_bounds(
  point_estimate = pf$point_estimate,
  conf_level = 0.8
)
pf$parameters

Method set_grid()

Computes a tibble storing a regular centered grid of the parameter space.

Usage

PlausibilityFunction$set_grid(parameters, npoints = 20L)

Arguments

Examples

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {
  purrr::map(y, ~ .x - parameters[1])
}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$set_nperms(50)
pf$set_point_estimate(mean(y) - mean(x))
pf$set_parameter_bounds(
  point_estimate = pf$point_estimate,
  conf_level = 0.8
)
pf$set_grid(
  parameters = pf$parameters,
  npoints = 2L
)

Method evaluate_grid()

Updates the grid field with a pvalue column storing evaluations of the plausibility function on the regular centered grid of the parameter space.

Usage

PlausibilityFunction$evaluate_grid(grid, ncores = 1L)

Arguments

Examples

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {
  purrr::map(y, ~ .x - parameters[1])
}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$set_nperms(50)
pf$set_point_estimate(mean(y) - mean(x))
pf$set_parameter_bounds(
  point_estimate = pf$point_estimate,
  conf_level = 0.8
)
pf$set_grid(
  parameters = pf$parameters,
  npoints = 2L
)
pf$evaluate_grid(grid = pf$grid)

Method clone()

The objects of this class are cloneable with this method.

Usage

PlausibilityFunction$clone(deep = FALSE)

Arguments

Examples

## ------------------------------------------------
## Method `PlausibilityFunction$set_nperms`
## ------------------------------------------------

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {purrr::map(y, ~ .x - parameters[1])}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$nperms
pf$set_nperms(10000)
pf$nperms

## ------------------------------------------------
## Method `PlausibilityFunction$set_nperms_max`
## ------------------------------------------------

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {purrr::map(y, ~ .x - parameters[1])}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$nperms_max
pf$set_nperms_max(10000)
pf$nperms_max

## ------------------------------------------------
## Method `PlausibilityFunction$set_alternative`
## ------------------------------------------------

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {purrr::map(y, ~ .x - parameters[1])}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$alternative
pf$set_alternative("right_tail")
pf$alternative

## ------------------------------------------------
## Method `PlausibilityFunction$set_aggregator`
## ------------------------------------------------

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {purrr::map(y, ~ .x - parameters[1])}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$aggregator
pf$set_aggregator("fisher")
pf$aggregator

## ------------------------------------------------
## Method `PlausibilityFunction$set_pvalue_formula`
## ------------------------------------------------

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {
  purrr::map(y, ~ .x - parameters[1])
}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$pvalue_formula
pf$set_pvalue_formula("estimate")
pf$pvalue_formula

## ------------------------------------------------
## Method `PlausibilityFunction$get_value`
## ------------------------------------------------

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {purrr::map(y, ~ .x - parameters[1])}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$set_nperms(50)
pf$get_value(2)

## ------------------------------------------------
## Method `PlausibilityFunction$set_max_conf_level`
## ------------------------------------------------

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {
  purrr::map(y, ~ .x - parameters[1])
}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$max_conf_level
pf$set_max_conf_level(0.999)
pf$max_conf_level

## ------------------------------------------------
## Method `PlausibilityFunction$set_point_estimate`
## ------------------------------------------------

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {
  purrr::map(y, ~ .x - parameters[1])
}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$point_estimate
pf$set_point_estimate(mean(y) - mean(x))
pf$point_estimate

## ------------------------------------------------
## Method `PlausibilityFunction$set_parameter_bounds`
## ------------------------------------------------

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {
  purrr::map(y, ~ .x - parameters[1])
}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$set_nperms(50)
pf$set_point_estimate(point_estimate = mean(y) - mean(x))
pf$parameters
pf$set_parameter_bounds(
  point_estimate = pf$point_estimate,
  conf_level = 0.8
)
pf$parameters

## ------------------------------------------------
## Method `PlausibilityFunction$set_grid`
## ------------------------------------------------

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {
  purrr::map(y, ~ .x - parameters[1])
}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$set_nperms(50)
pf$set_point_estimate(mean(y) - mean(x))
pf$set_parameter_bounds(
  point_estimate = pf$point_estimate,
  conf_level = 0.8
)
pf$set_grid(
  parameters = pf$parameters,
  npoints = 2L
)

## ------------------------------------------------
## Method `PlausibilityFunction$evaluate_grid`
## ------------------------------------------------

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {
  purrr::map(y, ~ .x - parameters[1])
}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$set_nperms(50)
pf$set_point_estimate(mean(y) - mean(x))
pf$set_parameter_bounds(
  point_estimate = pf$point_estimate,
  conf_level = 0.8
)
pf$set_grid(
  parameters = pf$parameters,
  npoints = 2L
)
pf$evaluate_grid(grid = pf$grid)

Create a biregular grid around a center point

Description

Biregular grids can be created for any number of parameter objects.

Usage

grid_biregular(
  x,
  ...,
  center = NULL,
  levels = 3,
  original = TRUE,
  filter = NULL
)

Arguments

Details

Note that there may a difference in grids depending on how the function is called. If the call uses the parameter objects directly the possible ranges come from the objects in dials. For example:

mixture()

## Proportion of Lasso Penalty (quantitative)
## Range: [0, 1]

set.seed(283)
mix_grid_1 <- grid_random(mixture(), size = 1000)
range(mix_grid_1$mixture)

## [1] 0.001490161 0.999741096

However, in some cases, the parsnip and recipe packages overrides the default ranges for specific models and preprocessing steps. If the grid function uses a parameters object created from a model or recipe, the ranges may have different defaults (specific to those models). Using the example above, the mixture argument above is different for glmnet models:

library(parsnip)
library(tune)

# When used with glmnet, the range is [0.05, 1.00]
glmn_mod <-
  linear_reg(mixture = tune()) %>%
  set_engine("glmnet")

set.seed(283)
mix_grid_2 <- grid_random(extract_parameter_set_dials(glmn_mod), size = 1000)
range(mix_grid_2$mixture)

## [1] 0.05141565 0.99975404

Value

A tibble. There are columns for each parameter and a row for every parameter combination.

Examples

grid_biregular(dials::mixture(), center = 0.2)

Test Statistics for the One-Sample Problem

Description

This is a collection of functions that provide test statistics to be used into the permutation scheme for performing one-sample testing.

Usage

stat_max(data, flips, ...)

Arguments

Value

A numeric value evaluating the desired test statistic.

Examples

n <- 10
x <- as.list(rnorm(n))
flips <- sample(c(-1, 1), n, replace = TRUE)
stat_max(x, flips)

One-Sample Permutation Test

Description

This function carries out an hypothesis test where the null hypothesis is that the sample is governed by a generative probability distribution which is centered and symmetric against the alternative hypothesis that they are governed by a probability distribution that is either not centered or not symmetric.

Usage

one_sample_test(
  x,
  stats = list(stat_max),
  B = 1000L,
  M = NULL,
  alternative = "two_tail",
  combine_with = "tippett",
  type = "exact",
  seed = NULL,
  ...
)

Arguments

Value

A list with three components: the value of the statistic for the original two samples, the p-value of the resulting permutation test and a numeric vector storing the values of the permuted statistics.

User-supplied statistic function

A user-specified function should have at least two arguments:

• the first argument is data which should be a list of the n observations from the sample;

• the second argument is flips which should be an integer vector giving the signs by which each observation in data should be multiplied.

It is possible to use the use_stat function with nsamples = 1 to have flipr automatically generate a template file for writing down your own test statistics in a way that makes it compatible with the flipr framework.

See the stat_max function for an example.

Examples

n <- 10L
mu <- 3
sigma <- 1

# Sample under the null distribution
x1 <- rnorm(n = n, mean = 0, sd = sigma)
t1 <- one_sample_test(x1, B = 100L)
t1$pvalue

# Sample under some alternative distribution
x2 <- rnorm(n = n, mean = mu, sd = sigma)
t2 <- one_sample_test(x2, B = 100L)
t2$pvalue

Visualization of Plausibility Functions

Description

This function plots the plausibility function for up to two parameters of interest.

Usage

plot_pf(pf, alpha = 0.05, ngrid = 10, ncores = 1, subtitle = "")

Arguments

Value

A ggplot object.

Examples

x <- rnorm(10)
y <- rnorm(10, mean = 2)
null_spec <- function(y, parameters) {purrr::map(y, ~ .x - parameters[1])}
stat_functions <- list(stat_t)
stat_assignments <- list(mean = 1)
pf <- PlausibilityFunction$new(
  null_spec = null_spec,
  stat_functions = stat_functions,
  stat_assignments = stat_assignments,
  x, y
)
pf$set_nperms(50)
pf$set_point_estimate(mean(y) - mean(x))
pf$set_parameter_bounds(
  point_estimate = pf$point_estimate,
  conf_level = 0.8
)
pf$set_grid(
  parameters = pf$parameters,
  npoints = 2L
)
pf$evaluate_grid(grid = pf$grid)
plot_pf(pf)

Test Statistics for the Two-Sample Problem

Description

This is a collection of functions that provide test statistics to be used into the permutation scheme for performing two-sample testing. These test statistics can be divided into two categories: traditional statistics that use empirical moments and inter-point statistics that only rely on pairwise dissimilarities between data points.

Usage

stat_welch(data, indices1, ...)

stat_student(data, indices1, ...)

stat_t(data, indices1, ...)

stat_fisher(data, indices1, ...)

stat_f(data, indices1, ...)

stat_mean(data, indices1, ...)

stat_hotelling(data, indices1, ...)

stat_bs(data, indices1, ...)

stat_student_ip(data, indices1, ...)

stat_t_ip(data, indices1, ...)

stat_fisher_ip(data, indices1, ...)

stat_f_ip(data, indices1, ...)

stat_bg_ip(data, indices1, ...)

stat_energy_ip(data, indices1, alpha = 1L, ...)

stat_cq_ip(data, indices1, ...)

stat_mod_ip(data, indices1, ...)

stat_dom_ip(data, indices1, standardize = TRUE, ...)

Arguments

Value

A real scalar giving the value of test statistic for the permutation specified by the integer vector indices.

Traditional Test Statistics

• stat_hotelling implements Hotelling's T^2 statistic for multivariate data with p < n.

• stat_student or stat_t implements Student's statistic (originally assuming equal variances and thus using the pooled empirical variance estimator). See t.test for details.

• stat_welch implements Student-Welch statistic which is essentially a modification of Student's statistic accounting for unequal variances. See t.test for details.

• stat_fisher or stat_f implements Fisher's variance ratio statistic. See var.test for details.

• stat_mean implements a statistic that computes the difference between the means.

• stat_bs implements the statistic proposed by Bai & Saranadasa (1996) for high-dimensional multivariate data.

Inter-Point Test Statistics

• stat_student_ip or stat_t_ip implements a Student-like test statistic based on inter-point distances only as described in Lovato et al. (2020).

• stat_fisher_ip or stat_f_ip implements a Fisher-like test statistic based on inter-point distances only as described in Lovato et al. (2020).

• stat_bg_ip implements the statistic proposed by Biswas & Ghosh (2014).

• stat_energy_ip implements the class of energy-based statistics as described in Székely & Rizzo (2013);

• stat_cq_ip implements the statistic proposed by Chen & Qin (2010).

• stat_mod_ip implements a statistic that computes the mean of inter-point distances.

• stat_dom_ip implements a statistic that computes the distance between the medoids of the two samples, possibly standardized by the pooled corresponding variances.

References

Bai, Z., & Saranadasa, H. (1996). Effect of high dimension: by an example of a two sample problem. Statistica Sinica, 311-329.

Lovato, I., Pini, A., Stamm, A., & Vantini, S. (2020). Model-free two-sample test for network-valued data. Computational Statistics & Data Analysis, 144, 106896.

Biswas, M., & Ghosh, A. K. (2014). A nonparametric two-sample test applicable to high dimensional data. Journal of Multivariate Analysis, 123, 160-171.

Székely, G. J., & Rizzo, M. L. (2013). Energy statistics: A class of statistics based on distances. Journal of statistical planning and inference, 143(8), 1249-1272.

Chen, S. X., & Qin, Y. L. (2010). A two-sample test for high-dimensional data with applications to gene-set testing. The Annals of Statistics, 38(2), 808-835.

Examples

n <- 10L
mx <- 0
sigma <- 1
delta <- 10
my <- mx + delta
x <- rnorm(n = n, mean = mx, sd = sigma)
y <- rnorm(n = n, mean = my, sd = sigma)
D <- dist(c(x, y))

x <- as.list(x)
y <- as.list(y)

stat_welch(c(x, y), 1:n)
stat_t(c(x, y), 1:n)
stat_f(c(x, y), 1:n)
stat_mean(c(x, y), 1:n)
stat_hotelling(c(x, y), 1:n)
stat_bs(c(x, y), 1:n)

stat_t_ip(D, 1:n)
stat_f_ip(D, 1:n)
stat_bg_ip(D, 1:n)
stat_energy_ip(D, 1:n)
stat_cq_ip(D, 1:n)
stat_mod_ip(D, 1:n)
stat_dom_ip(D, 1:n)

Two-Sample Permutation Test

Description

This function carries out an hypothesis test in which the null hypothesis is that the two samples are governed by the same underlying generative probability distribution against the alternative hypothesis that they are governed by two different generative probability distributions.

Usage

two_sample_test(
  x,
  y,
  stats = list(stat_t),
  B = 1000L,
  M = NULL,
  alternative = "two_tail",
  combine_with = "tippett",
  type = "exact",
  seed = NULL,
  ...
)

Arguments

Value

A list with three components: the value of the statistic for the original two samples, the p-value of the resulting permutation test and a numeric vector storing the values of the permuted statistics.

User-supplied statistic function

A user-specified function should have at least two arguments:

• the first argument is data which should be a list of the n1 + n2 concatenated observations with the original n1 observations from the first sample on top and the original n2 observations from the second sample below;

• the second argument is perm_data which should be an integer vector giving the indices in data that are considered to belong to the first sample.

It is possible to use the use_stat function with nsamples = 2 to have flipr automatically generate a template file for writing down your own test statistics in a way that makes it compatible with the flipr framework.

See the stat_t function for an example.

Examples

n <- 10L
mx <- 0
sigma <- 1

# Two different models for the two populations
x <- rnorm(n = n, mean = mx, sd = sigma)
delta <- 10
my <- mx + delta
y <- rnorm(n = n, mean = my, sd = sigma)
t1 <- two_sample_test(x, y)
t1$pvalue

# Same model for the two populations
x <- rnorm(n = n, mean = mx, sd = sigma)
delta <- 0
my <- mx + delta
y <- rnorm(n = n, mean = my, sd = sigma)
t2 <- two_sample_test(x, y)
t2$pvalue

Test Statistic Template

Description

This function is a helper to automatically generate an .R file populated with a skeleton of a typical test function compatible with flipr.

Usage

use_stat(nsamples = 1, stat_name = "mystat")

Arguments

Value

Creates a dedicated .R file with a template of code for the function that implements the test statistic and saves it to the ⁠R/⁠ folder of your package.

Examples

## Not run: 
use_stat()

## End(Not run)