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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 ORCID iD [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

X

A matrix of observations (design matrix) with size n x p

Y

A vector of responses with length n

alpha

The significance level for confidence intervals

K

The number of subsets to consider

nk

The size of each subset

Value

A list containing:

E5

The LIC estimator based on A-optimal and D-optimal criterion.

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

X

is a design matrix

Y

is a random response vector of observed values

alpha

is the significance level

K

is the number of subsets

nk

is the sample size of subsets

dist_type

is the type where the error term obeys a T-distribution

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

K

is the number of subsets

nk

is the length of subsets

alpha

is the significance level

X

is the observation matrix

y

is the response vector

Value

A list containing:

betaA

The estimator of beta on the A-opt.

betaD

The estimator of beta on the D-opt.

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

K

is the number of subsets

nk

is the length of subsets

alpha

is the significance level

X

is the observation matrix

y

is the response vector

Value

A list containing:

betaC

The estimator of beta on the COR.

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

n

is the number of observations

nr

is the number of observations with a different error T distribution

p

is the dimension of the observation

dist_type

is the type where the error term obeys a T-distribution

...

is additional arguments for the T-distribution function

Value

X,Y,e

Examples

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

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They may not be fully stable and should be used with caution. We make no claims about them.
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