| Type: | Package |
| Title: | Quantile, Composite Quantile Regression and Regularized Versions |
| Version: | 1.2.1 |
| Date: | 2022-06-07 |
| Author: | Jueyu Gao & Linglong Kong |
| Maintainer: | Jueyu Gao <jueyu@ualberta.ca> |
| Description: | Estimate quantile regression(QR) and composite quantile regression (cqr) and with adaptive lasso penalty using interior point (IP), majorize and minimize(MM), coordinate descent (CD), and alternating direction method of multipliers algorithms(ADMM). |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Depends: | Rcpp (≥ 0.10.0),quantreg,R (≥ 2.6) |
| LinkingTo: | Rcpp,RcppArmadillo |
| NeedsCompilation: | yes |
| Packaged: | 2022-06-07 00:19:21 UTC; neoga |
| Repository: | CRAN |
| Date/Publication: | 2022-06-07 05:00:02 UTC |
Composite Quantile regression (cqr) use Alternating Direction Method of Multipliers (ADMM) algorithm core computational part
Description
Composite quantile regression (cqr) find the estimated coefficient which minimize the absolute error for various quantile level. The problem is well suited to distributed convex optimization and is based on Alternating Direction Method of Multipliers (ADMM) algorithm .
Composite Quantile Regression (cqr) use Coordinate Descent (cd) Algorithms core computational part
Description
Composite quantile regression (cqr) find the estimated coefficient which minimize the absolute error for various quantile level.
The algorithm base on greedy coordinate descent and Edgeworth's for ordinary l_1 regression.
Composite Quantile Regression (cqr) use Majorize and Minimize (mm) Algorithm core computational part
Description
Composite quantile regression find the estimated coefficient which minimize the absolute error for various quantile level. The algorithm majorizing the objective function by a quadratic function followed by minimizing that quadratic.
Composite Quantile Regression (cqr) with Adaptive Lasso Penalty (lasso) use Alternating Direction Method of Multipliers (ADMM) algorithm core computational part
Description
The adaptive lasso parameter base on the estimated coefficient without penalty function. Composite quantile regression find the estimated coefficient which minimize the absolute error for various quantile level. The problem is well suited to distributed convex optimization and is based on Alternating Direction Method of Multipliers (ADMM) algorithm .
Composite Quantile Regression (cqr) with Adaptive Lasso Penalty (lasso) use Coordinate Descent (cd) Algorithms core computational part
Description
The adaptive lasso parameter base on the estimated coefficient without penalty function.
Composite quantile regression find the estimated coefficient which minimize the absolute error for various quantile level.
The algorithm base on greedy coordinate descent and Edgeworth's for ordinary l_1 regression.
Composite Quantile Regression (cqr) with Adaptive Lasso Penalty (lasso) use Majorize and Minimize (mm) Algorithm core computational part
Description
The adaptive lasso penalty parameter base on the estimated coefficient without penalty function. Composite quantile regression find the estimated coefficient which minimize the absolute error for various quantile level. The algorithm majorizing the objective function by a quadratic function followed by minimizing that quadratic.
Quantile Regression (QR) use Alternating Direction Method of Multipliers (ADMM) algorithm
Description
The problem is well suited to distributed convex optimization and is based on Alternating Direction Method of Multipliers (ADMM) algorithm .
Usage
QR.admm(X,y,tau,rho,beta, maxit, toler)
Arguments
X |
the design matrix |
y |
response variable |
tau |
quantile level |
rho |
augmented Lagrangian parameter |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
toler |
the tolerance critical for stop the algorithm (default 1e-3) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
QR.admm(x,y,tau) work properly only if the least square estimation is good.
References
S. Boyd, N. Parikh, E. Chu, B. Peleato and J. Eckstein.(2010) Distributed Optimization and Statistical Learning via the Alternating Direction.Method of Multipliers Foundations and Trends in Machine Learning, 3, No.1, 1–122
Koenker, Roger. Quantile Regression, New York, 2005. Print.
Examples
set.seed(1)
n=100
p=2
a=rnorm(n*p, mean = 1, sd =1)
x=matrix(a,n,p)
beta=rnorm(p,1,1)
beta=matrix(beta,p,1)
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
# x is 1000*10 matrix, y is 1000*1 vector, beta is 10*1 vector
QR.admm(x,y,0.1)
Quantile Regression (QR) use Coordinate Descent (cd) Algorithms
Description
The algorithm base on greedy coordinate descent and Edgeworth's for ordinary l_1 regression.
Usage
QR.cd(X,y,tau,beta,maxit,toler)
Arguments
X |
the design matrix |
y |
response variable |
tau |
quantile level |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
toler |
the tolerance critical for stop the algorithm (default 1e-3) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
QR.cd(x,y,tau) work properly only if the least square estimation is good.
References
Wu, T.T. and Lange, K. (2008). Coordinate Descent Algorithms for Lasso Penalized Regression. Annals of Applied Statistics, 2, No 1, 224–244.
Koenker, Roger. Quantile Regression, New York, 2005. Print.
Examples
set.seed(1)
n=100
p=2
a=rnorm(n*p, mean = 1, sd =1)
x=matrix(a,n,p)
beta=rnorm(p,1,1)
beta=matrix(beta,p,1)
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
# x is 1000*10 matrix, y is 1000*1 vector, beta is 10*1 vector
QR.cd(x,y,0.1)
Quantile Regression (QR) use Interior Point (ip) Method
Description
The function use the interior point method from quantreg to solve the quantile regression problem.
Usage
QR.ip(X,y,tau)
Arguments
X |
the design matrix |
y |
response variable |
tau |
quantile level |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
Need to install quantreg package from CRAN.
References
Koenker, Roger. Quantile Regression, New York, 2005. Print.
Koenker, R. and S. Portnoy (1997). The Gaussian Hare and the Laplacian Tortoise: Computability of squared-error vs. absolute-error estimators, with discussion, Statistical Science, 12, 279-300.
Examples
set.seed(1)
n=100
p=2
a=rnorm(n*p, mean = 1, sd =1)
x=matrix(a,n,p)
beta=rnorm(p,1,1)
beta=matrix(beta,p,1)
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
# x is 1000*10 matrix, y is 1000*1 vector, beta is 10*1 vector
#you should install Rmosek first to run following command
#QR.ip(x,y,0.1)
Quantile Regression (QR) with Adaptive Lasso Penalty (lasso) use Alternating Direction Method of Multipliers (ADMM) algorithm
Description
The adaptive lasso parameter base on the estimated coefficient without penalty function. The problem is well suited to distributed convex optimization and is based on Alternating Direction Method of Multipliers (ADMM) algorithm .
Usage
QR.lasso.admm(X,y,tau,lambda,rho,beta,maxit)
Arguments
X |
the design matrix |
y |
response variable |
tau |
quantile level |
lambda |
The constant coefficient of penalty function. (default lambda=1) |
rho |
augmented Lagrangian parameter |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
QR.lasso.admm(x,y,tau) work properly only if the least square estimation is good.
References
S. Boyd, N. Parikh, E. Chu, B. Peleato and J. Eckstein.(2010) Distributed Optimization and Statistical Learning via the Alternating Direction. Method of Multipliers Foundations and Trends in Machine Learning, 3, No.1, 1–122
Wu, Yichao and Liu, Yufeng (2009). Variable selection in quantile regression. Statistica Sinica, 19, 801–817.
Examples
set.seed(1)
n=100
p=2
a=2*rnorm(n*2*p, mean = 1, sd =1)
x=matrix(a,n,2*p)
beta=2*rnorm(p,1,1)
beta=rbind(matrix(beta,p,1),matrix(0,p,1))
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
# x is 1000*20 matrix, y is 1000*1 vector, beta is 20*1 vector with last ten zero value elements.
QR.lasso.admm(x,y,0.1)
Quantile Regression (QR) with Adaptive Lasso Penalty (lasso) use Coordinate Descent (cd) Algorithms
Description
The adaptive lasso parameter base on the estimated coefficient without penalty function.
The algorithm base on greedy coordinate descent and Edgeworth's for ordinary l_1 regression. As explored by Tong Tong Wu and Kenneth Lange.
Usage
QR.lasso.cd(X,y,tau,lambda,beta,maxit,toler)
Arguments
X |
the design matrix |
y |
response variable |
tau |
quantile level |
lambda |
The constant coefficient of penalty function. (default lambda=1) |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
toler |
the tolerance critical for stop the algorithm (default 1e-3) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
QR.lasso.cd(x,y,tau) work properly only if the least square estimation is good.
References
Wu, T.T. and Lange, K. (2008). Coordinate Descent Algorithms for Lasso Penalized Regression. Annals of Applied Statistics, 2, No 1, 224–244.
Wu, Yichao and Liu, Yufeng (2009). Variable selection in quantile regression. Statistica Sinica, 19, 801–817.
Examples
set.seed(1)
n=100
p=2
a=2*rnorm(n*2*p, mean = 1, sd =1)
x=matrix(a,n,2*p)
beta=2*rnorm(p,1,1)
beta=rbind(matrix(beta,p,1),matrix(0,p,1))
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
# x is 1000*20 matrix, y is 1000*1 vector, beta is 20*1 vector with last ten zero value elements.
QR.lasso.cd(x,y,0.1)
Quantile Regression (QR) with Adaptive Lasso Penalty (lasso) use Interior Point (ip) Method
Description
The function use the interior point method from quantreg to solve the quantile regression problem.
Usage
QR.lasso.ip(X,y,tau,lambda)
Arguments
X |
the design matrix |
y |
response variable |
tau |
quantile level |
lambda |
The constant coefficient of penalty function. (default lambda=1) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
lambda |
The constant coefficient of penalty function. (default lambda=1) |
Note
Need to install quantreg package from CRAN.
References
Koenker, R. and S. Portnoy (1997). The Gaussian Hare and the Laplacian Tortoise: Computability of squared-error vs. absolute-error estimators, with discussion, Statistical Science, 12, 279-300.
Wu, Yichao and Liu, Yufeng (2009). Variable selection in quantile regression. Statistica Sinica, 19, 801–817.
Examples
set.seed(1)
n=100
p=2
a=2*rnorm(n*2*p, mean = 1, sd =1)
x=matrix(a,n,2*p)
beta=2*rnorm(p,1,1)
beta=rbind(matrix(beta,p,1),matrix(0,p,1))
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
# x is 1000*20 matrix, y is 1000*1 vector, beta is 20*1 vector with last ten zero value elements.
#you should install Rmosek first to run following command
#QR.lasso.ip(x,y,0.1)
Quantile Regression (QR) with Adaptive Lasso Penalty (lasso) use Majorize and Minimize (mm) algorithm
Description
The adaptive lasso parameter base on the estimated coefficient without penalty function. The algorithm majorizing the objective function by a quadratic function followed by minimizing that quadratic.
Usage
QR.lasso.mm(X,y,tau,lambda,beta,maxit,toler)
Arguments
X |
the design matrix. |
y |
response variable. |
tau |
quantile level. |
lambda |
The constant coefficient of penalty function. (default lambda=1) |
beta |
initial value of estimate coefficient.(default naive guess by least square estimation) |
maxit |
maxim iteration. (default 200) |
toler |
the tolerance critical for stop the algorithm. (default 1e-3) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
QR.lasso.mm(x,y,tau) work properly only if the least square estimation is good.
References
David R.Hunter and Runze Li.(2005) Variable Selection Using MM Algorithms,The Annals of Statistics 33, Number 4, Page 1617–1642.
Examples
set.seed(1)
n=100
p=2
a=2*rnorm(n*2*p, mean = 1, sd =1)
x=matrix(a,n,2*p)
beta=2*rnorm(p,1,1)
beta=rbind(matrix(beta,p,1),matrix(0,p,1))
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
# x is 1000*20 matrix, y is 1000*1 vector, beta is 20*1 vector with last ten zero value elements.
QR.lasso.mm(x,y,0.1)
Quantile Regression (QR) use Majorize and Minimize (mm) algorithm
Description
The algorithm majorizing the objective function by a quadratic function followed by minimizing that quadratic.
Usage
QR.mm(X,y,tau,beta,maxit,toler)
Arguments
X |
the design matrix |
y |
response variable |
tau |
quantile level |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
toler |
the tolerance critical for stop the algorithm (default 1e-3) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
QR.mm(x,y,tau) work properly only if the least square estimation is good.
References
David R.Hunter and Kenneth Lange. Quantile Regression via an MM Algorithm, Journal of Computational and Graphical Statistics, 9, Number 1, Page 60–77
Examples
set.seed(1)
n=100
p=2
a=rnorm(n*p, mean = 1, sd =1)
x=matrix(a,n,p)
beta=rnorm(p,1,1)
beta=matrix(beta,p,1)
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
# x is 1000*10 matrix, y is 1000*1 vector, beta is 10*1 vector
QR.mm(x,y,0.1)
Quantile Regression (QR) use Alternating Direction Method of Multipliers (ADMM) algorithm core computational part
Description
The problem is well suited to distributed convex optimization and is based on Alternating Direction Method of Multipliers (ADMM) algorithm .
Quantile Regression (QR) use Coordinate Descent (cd) Algorithms core computational part
Description
The algorithm base on greedy coordinate descent and Edgeworth's for ordinary l_1 regression.
Quantile Regression (QR) use Majorize and Minimize (mm) algorithm core computational part
Description
The algorithm majorizing the objective function by a quadratic function followed by minimizing that quadratic.
Quantile Regression (QR) with Adaptive Lasso Penalty (lasso) use Alternating Direction Method of Multipliers (ADMM) algorithm core computational part
Description
The adaptive lasso parameter base on the estimated coefficient without penalty function. The problem is well suited to distributed convex optimization and is based on Alternating Direction Method of Multipliers (ADMM) algorithm .
Quantile Regression (QR) with Adaptive Lasso Penalty (lasso) use Coordinate Descent (cd) Algorithms core computational part
Description
The adaptive lasso parameter base on the estimated coefficient without penalty function.
The algorithm base on greedy coordinate descent and Edgeworth's for ordinary l_1 regression. As explored by Tong Tong Wu and Kenneth Lange.
Quantile Regression (QR) with Adaptive Lasso Penalty (lasso) use Majorize and Minimize (mm) algorithm core computational part
Description
The adaptive lasso parameter base on the estimated coefficient without penalty function. The algorithm majorizing the objective function by a quadratic function followed by minimizing that quadratic.
Composite Quantile regression (cqr) use Alternating Direction Method of Multipliers (ADMM) algorithm.
Description
Composite quantile regression (cqr) find the estimated coefficient which minimize the absolute error for various quantile level. The problem is well suited to distributed convex optimization and is based on Alternating Direction Method of Multipliers (ADMM) algorithm .
Usage
cqr.admm(X,y,tau,rho,beta, maxit, toler)
Arguments
X |
the design matrix |
y |
response variable |
tau |
vector of quantile level |
rho |
augmented Lagrangian parameter |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
toler |
the tolerance critical for stop the algorithm (default 1e-3) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
cqr.admm(x,y,tau) work properly only if the least square estimation is good.
References
S. Boyd, N. Parikh, E. Chu, B. Peleato and J. Eckstein.(2010) Distributed Optimization and Statistical Learning via the Alternating Direction. Method of Multipliers Foundations and Trends in Machine Learning, 3, No. 1, 1–122
Hui Zou and Ming Yuan(2008). Composite Quantile Regression and the Oracle Model Selection Theory, The Annals of Statistics, 36, Number 3, Page 1108–1126.
Examples
set.seed(1)
n=100
p=2
a=rnorm(n*p, mean = 1, sd =1)
x=matrix(a,n,p)
beta=rnorm(p,1,1)
beta=matrix(beta,p,1)
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
tau=1:5/6
# x is 1000*10 matrix, y is 1000*1 vector, beta is 10*1 vector
cqr.admm(x,y,tau)
Composite Quantile Regression (cqr) use Coordinate Descent (cd) Algorithms
Description
Composite quantile regression (cqr) find the estimated coefficient which minimize the absolute error for various quantile level.
The algorithm base on greedy coordinate descent and Edgeworth's for ordinary l_1 regression.
Usage
cqr.cd(X,y,tau,beta,maxit,toler)
Arguments
X |
the design matrix |
y |
response variable |
tau |
vector of quantile level |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
toler |
the tolerance critical for stop the algorithm (default 1e-3) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
cqr.cd(x,y,tau) work properly only if the least square estimation is good.
References
Wu, T.T. and Lange, K. (2008). Coordinate Descent Algorithms for Lasso Penalized Regression. Annals of Applied Statistics, 2, No 1, 224–244.
Hui Zou and Ming Yuan(2008). Composite Quantile Regression and the Oracle Model Selection Theory, The Annals of Statistics, 36, Number 3, Page 1108–1126.
Examples
set.seed(1)
n=100
p=2
a=rnorm(n*p, mean = 1, sd =1)
x=matrix(a,n,p)
beta=rnorm(p,1,1)
beta=matrix(beta,p,1)
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
tau=1:5/6
# x is 1000*10 matrix, y is 1000*1 vector, beta is 10*1 vector
cqr.cd(x,y,tau)
Composite Quantile Regression (cqr) model fitting
Description
Composite quantile regression (cqr) find the estimated coefficient which minimize the absolute error for various quantile level. High level function for estimating parameter by composite quantile regression.
Usage
cqr.fit(X,y,tau,beta,method,maxit,toler,rho)
Arguments
X |
the design matrix |
y |
response variable |
tau |
vector of quantile level |
method |
"mm" for majorize and minimize method,"cd" for coordinate descent method, "admm" for Alternating method of mulipliers method,"ip" for interior point mehod |
rho |
augmented Lagrangian parameter |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
toler |
the tolerance critical for stop the algorithm (default 1e-3) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
cqr.fit(x,y,tau) work properly only if the least square estimation is good. Interior point method is done by quantreg.
Composite Quantile Regression (cqr) with Adaptive Lasso Penalty (lasso)
Description
Composite quantile regression (cqr) find the estimated coefficient which minimize the absolute error for various quantile level. High level function for estimating and selecting parameter by composite quantile regression with adaptive lasso penalty.
Usage
cqr.fit.lasso(X,y,tau,lambda,beta,method,maxit,toler,rho)
Arguments
X |
the design matrix |
y |
response variable |
tau |
vector of quantile level |
method |
"mm" for majorize and minimize method,"cd" for coordinate descent method, "admm" for Alternating method of mulipliers method |
lambda |
The constant coefficient of penalty function. (default lambda=1) |
rho |
augmented Lagrangian parameter |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
toler |
the tolerance critical for stop the algorithm (default 1e-3) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
cqr.fit.lasso(x,y,tau) work properly only if the least square estimation is good.
Composite Quantile Regression (cqr) use Interior Point (ip) Method
Description
The function use the interior point method from quantreg to solve the quantile regression problem.
Usage
cqr.ip(X,y,tau)
Arguments
X |
the design matrix |
y |
response variable |
tau |
vector of quantile level |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
Need to install quantreg package from CRAN.
References
Koenker, R. and S. Portnoy (1997). The Gaussian Hare and the Laplacian Tortoise: Computability of squared-error vs. absolute-error estimators, with discussion, Statistical Science, 12, 279-300.
Hui Zou and Ming Yuan(2008). Composite Quantile Regression and the Oracle Model Selection Theory, The Annals of Statistics, 36, Number 3, Page 1108–1126.
Examples
set.seed(1)
n=100
p=2
a=rnorm(n*p, mean = 1, sd =1)
x=matrix(a,n,p)
beta=rnorm(p,1,1)
beta=matrix(beta,p,1)
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
tau=1:5/6
# x is 1000*10 matrix, y is 1000*1 vector, beta is 10*1 vector
#you should install quantreg first to run following command
#cqr.ip(x,y,tau)
Composite Quantile Regression (cqr) with Adaptive Lasso Penalty (lasso) use Alternating Direction Method of Multipliers (ADMM) algorithm
Description
The adaptive lasso parameter base on the estimated coefficient without penalty function. Composite quantile regression find the estimated coefficient which minimize the absolute error for various quantile level. The problem is well suited to distributed convex optimization and is based on Alternating Direction Method of Multipliers (ADMM) algorithm .
Usage
cqr.lasso.admm(X,y,tau,lambda,rho,beta,maxit)
Arguments
X |
the design matrix |
y |
response variable |
tau |
vector of quantile level |
lambda |
The constant coefficient of penalty function. (default lambda=1) |
rho |
augmented Lagrangian parameter |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
cqr.lasso.admm(x,y,tau) work properly only if the least square estimation is good.
References
S. Boyd, N. Parikh, E. Chu, B. Peleato and J. Eckstein.(2010) Distributed Optimization and Statistical Learning via the Alternating Direction. Method of Multipliers Foundations and Trends in Machine Learning, 3, No. 1, 1–122
Hui Zou and Ming Yuan(2008). Composite Quantile Regression and the Oracle Model Selection Theory, The Annals of Statistics, 36, Number 3, Page 1108–1126.
Examples
set.seed(1)
n=100
p=2
a=2*rnorm(n*2*p, mean = 1, sd =1)
x=matrix(a,n,2*p)
beta=2*rnorm(p,1,1)
beta=rbind(matrix(beta,p,1),matrix(0,p,1))
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
tau=1:5/6
# x is 1000*20 matrix, y is 1000*1 vector, beta is 20*1 vector with last ten zero value elements.
cqr.lasso.admm(x,y,tau)
Composite Quantile Regression (cqr) with Adaptive Lasso Penalty (lasso) use Coordinate Descent (cd) Algorithms
Description
The adaptive lasso parameter base on the estimated coefficient without penalty function.
Composite quantile regression find the estimated coefficient which minimize the absolute error for various quantile level.
The algorithm base on greedy coordinate descent and Edgeworth's for ordinary l_1 regression.
Usage
cqr.lasso.cd(X,y,tau,lambda,beta,maxit,toler)
Arguments
X |
the design matrix |
y |
response variable |
tau |
vector of quantile level |
lambda |
The constant coefficient of penalty function. (default lambda=1) |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
toler |
the tolerance critical for stop the algorithm (default 1e-3) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
cqr.lasso.cd(x,y,tau) work properly only if the least square estimation is good.
References
Wu, T.T. and Lange, K. (2008). Coordinate Descent Algorithms for Lasso Penalized Regression. Annals of Applied Statistics, 2, No 1, 224–244.
Hui Zou and Ming Yuan(2008). Composite Quantile Regression and the Oracle Model Selection Theory, The Annals of Statistics, 36, Number 3, Page 1108–1126.
Examples
set.seed(1)
n=100
p=2
a=2*rnorm(n*2*p, mean = 1, sd =1)
x=matrix(a,n,2*p)
beta=2*rnorm(p,1,1)
beta=rbind(matrix(beta,p,1),matrix(0,p,1))
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
tau=1:5/6
# x is 1000*20 matrix, y is 1000*1 vector, beta is 20*1 vector with last ten zero value elements.
cqr.lasso.cd(x,y,tau)
Composite Quantile Regression (cqr) with Adaptive Lasso Penalty (lasso) use Majorize and Minimize (mm) Algorithm
Description
The adaptive lasso penalty parameter base on the estimated coefficient without penalty function. Composite quantile regression find the estimated coefficient which minimize the absolute error for various quantile level. The algorithm majorizing the objective function by a quadratic function followed by minimizing that quadratic.
Usage
cqr.lasso.mm(X,y,tau,lambda,beta,maxit,toler)
Arguments
X |
the design matrix |
y |
response variable |
tau |
vector of quantile level |
lambda |
The constant coefficient of penalty function. (default lambda=1) |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
toler |
the tolerance critical for stop the algorithm (default 1e-3) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept for various quantile level |
Note
cqr.lasso.mm(x,y,tau) work properly only if the least square estimation is good.
References
David R.Hunter and Runze Li.(2005) Variable Selection Using MM Algorithms,The Annals of Statistics 33, Number 4, Page 1617–1642.
Hui Zou and Ming Yuan(2008). Composite Quantile Regression and the Oracle Model Selection Theory, The Annals of Statistics, 36, Number 3, Page 1108–1126.
Examples
set.seed(1)
n=100
p=2
a=2*rnorm(n*2*p, mean = 1, sd =1)
x=matrix(a,n,2*p)
beta=2*rnorm(p,1,1)
beta=rbind(matrix(beta,p,1),matrix(0,p,1))
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
tau=1:5/6
# x is 1000*20 matrix, y is 1000*1 vector, beta is 20*1 vector with last ten zero value elements.
cqr.lasso.mm(x,y,tau)
Composite Quantile Regression (cqr) use Majorize and Minimize (mm) Algorithm
Description
Composite quantile regression find the estimated coefficient which minimize the absolute error for various quantile level. The algorithm majorizing the objective function by a quadratic function followed by minimizing that quadratic.
Usage
cqr.mm(X,y,tau,beta,maxit,toler)
Arguments
X |
the design matrix |
y |
response variable |
tau |
vector of quantile level |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
toler |
the tolerance critical for stop the algorithm (default 1e-3) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept for various quantile level |
Note
cqr.mm(x,y,tau) work properly only if the least square estimation is good.
References
David R.Hunter and Kenneth Lange. Quantile Regression via an MM Algorithm,Journal of Computational and Graphical Statistics, 9, Number 1, Page 60–77.
Hui Zou and Ming Yuan(2008). Composite Quantile Regression and the Oracle Model Selection Theory, The Annals of Statistics, 36, Number 3, Page 1108–1126.
Examples
set.seed(1)
n=100
p=2
a=rnorm(n*p, mean = 1, sd =1)
x=matrix(a,n,p)
beta=rnorm(p,1,1)
beta=matrix(beta,p,1)
y=x%*%beta-matrix(rnorm(n,0.1,1),n,1)
tau=1:5/6
# x is 1000*10 matrix, y is 1000*1 vector, beta is 10*1 vector
cqr.mm(x,y,tau)
Quantile Regression (qr) model fitting
Description
High level function for estimating parameters by quantile regression
Usage
qrfit(X,y,tau,beta,method,maxit,toler,rho)
Arguments
X |
the design matrix |
y |
response variable |
tau |
quantile level |
method |
"mm" for majorize and minimize method,"cd" for coordinate descent method, "admm" for Alternating method of mulipliers method,"ip" for interior point mehod |
rho |
augmented Lagrangian parameter |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
toler |
the tolerance critical for stop the algorithm (default 1e-3) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
qrfit(x,y,tau) work properly only if the least square estimation is good. Interior point method is done by quantreg.
Quantile Regression (qr) with Adaptive Lasso Penalty (lasso)
Description
High level function for estimating and selecting parameter by quantile regression with adaptive lasso penalty.
Usage
qrfit.lasso(X,y,tau,lambda,beta,method,maxit,toler,rho)
Arguments
X |
the design matrix |
y |
response variable |
tau |
quantile level |
method |
"mm" for majorize and minimize method,"cd" for coordinate descent method, "admm" for Alternating method of mulipliers method,"ip" for interior point mehod |
lambda |
The constant coefficient of penalty function. (default lambda=1) |
rho |
augmented Lagrangian parameter |
beta |
initial value of estimate coefficient (default naive guess by least square estimation) |
maxit |
maxim iteration (default 200) |
toler |
the tolerance critical for stop the algorithm (default 1e-3) |
Value
a list structure is with components
beta |
the vector of estimated coefficient |
b |
intercept |
Note
qrfit.lasso(x,y,tau) work properly only if the least square estimation is good. Interior point method is done by quantreg.