Type:	Package
Title:	The LIC for T Distribution Regression Analysis
Version:	0.4
Date:	2025-2-12
Description:	This comprehensive toolkit for T-distributed regression is designated as "TLIC" (The LIC for T Distribution Regression Analysis) analysis. It is predicated on the assumption that the error term adheres to a T-distribution. The philosophy of the package is described in Guo G. (2020) <doi:10.1080/02664763.2022.2053949>.
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.3.2
Imports:	stats, LaplacesDemon, fBasics
NeedsCompilation:	no
Author:	Guangbao Guo [aut, cre], Guofu Jing [aut]
Maintainer:	Guangbao Guo <ggb11111111@163.com>
Repository:	CRAN
Date/Publication:	2025-02-12 03:30:01 UTC
Packaged:	2025-02-11 13:28:58 UTC; A

Calculate the LIC estimator based on A-optimal and D-optimal criterion

Description

Calculate the LIC estimator based on A-optimal and D-optimal criterion

Usage

LICnew(X, Y, alpha, K, nk)

Arguments

Value

A list containing:

References

Guo, G., Song, H. & Zhu, L. The COR criterion for optimal subset selection in distributed estimation. Statistics and Computing, 34, 163 (2024). doi:10.1007/s11222-024-10471-z

Examples

p = 6; n = 1000; K = 2; nk = 200; alpha = 0.05; sigma = 1
e = rnorm(n, 0, sigma); beta = c(sort(c(runif(p, 0, 1))));
data = c(rnorm(n * p, 5, 10)); X = matrix(data, ncol = p);
Y = X %*% beta + e;
LICnew(X = X, Y = Y, alpha = alpha, K = K, nk = nk)

TLIC function based on LIC with T-distributed errors

Description

The TLIC function builds on the LIC function by introducing the assumption that the error term follows a T-distribution, thereby enhancing the length and information optimisation criterion.

Usage

TLIC(X, Y, alpha = 0.05, K = 10, nk = NULL, dist_type = "student_t")

Arguments

Value

MUopt, Bopt, MAEMUopt, MSEMUopt, opt, Yopt

Examples

set.seed(12)
n <- 1200
nr <- 200
p <- 5
data <- terr(n, nr, p, dist_type = "student_t")
TLIC(data$X, data$Y, alpha = 0.05, K = 10, nk = n / 10, dist_type = "student_t")

Caculate the estimators of beta on the A-opt and D-opt

Description

Caculate the estimators of beta on the A-opt and D-opt

Usage

beta_AD(K = K, nk = nk, alpha = alpha, X = X, y = y)

Arguments

Value

A list containing:

References

Guo, G., Song, H. & Zhu, L. The COR criterion for optimal subset selection in distributed estimation. Statistics and Computing, 34, 163 (2024). doi:10.1007/s11222-024-10471-z

Examples

 p=6;n=1000;K=2;nk=200;alpha=0.05;sigma=1
 e=rnorm(n,0,sigma); beta=c(sort(c(runif(p,0,1))));
 data=c(rnorm(n*p,5,10));X=matrix(data, ncol=p);
 y=X%*%beta+e;
 beta_AD(K=K,nk=nk,alpha=alpha,X=X,y=y)

Caculate the estimator of beta on the COR

Description

Caculate the estimator of beta on the COR

Usage

beta_cor(K = K, nk = nk, alpha = alpha, X = X, y = y)

Arguments

Value

A list containing:

References

Guo, G., Song, H. & Zhu, L. The COR criterion for optimal subset selection in distributed estimation. Statistics and Computing, 34, 163 (2024). doi:10.1007/s11222-024-10471-z

Examples

 p=6;n=1000;K=2;nk=200;alpha=0.05;sigma=1
 e=rnorm(n,0,sigma); beta=c(sort(c(runif(p,0,1))));
 data=c(rnorm(n*p,5,10));X=matrix(data, ncol=p);
 y=X%*%beta+e;
 beta_cor(K=K,nk=nk,alpha=alpha,X=X,y=y)

terr function is used to generate a dataset where the error term follows a T-distribution

Description

This terr function generates a dataset with a specified number of observations and predictors, along with a response vector that has an error term following a T-distribution.

Usage

terr(n, nr, p, dist_type, ...)

Arguments

Value

X,Y,e

Examples

set.seed(12)
data <- terr(n = 1200, nr = 200, p = 5, dist_type = "student_t")
str(data)