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Type: Package
Title: The LIC for Distributed Cosine Regression Analysis
Version: 0.1
Date: 2025-08-18
Description: This comprehensive framework for periodic time series modeling is designated as "CLIC" (The LIC for Distributed Cosine Regression Analysis) analysis. It is predicated on the assumption that the underlying data exhibits complex periodic structures beyond simple harmonic components. The philosophy of the method is articulated in Guo G. (2020) <doi:10.1080/02664763.2022.2053949>.
License: MIT + file LICENSE
Encoding: UTF-8
RoxygenNote: 7.3.2
Depends: R (≥ 3.5.0)
Imports: stats, LaplacesDemon, fBasics
Suggests: testthat (≥ 3.0.0)
NeedsCompilation: no
Author: Guangbao Guo ORCID iD [aut, cre], Pengbo Kong [aut]
Maintainer: Guangbao Guo <ggb11111111@163.com>
Config/testthat/edition: 3
Packaged: 2025-08-21 05:16:48 UTC; Kong Pengbo
Repository: CRAN
Date/Publication: 2025-08-27 11:00:08 UTC

CLIC function based on LIC with cosine_random distributed errors

Description

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

Usage

CLIC(X, Y, alpha = 0.05, K = 10, nk = NULL, dist_type = "cosine_random")

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 cosine_random distribution

Value

MUopt, Bopt, MAEMUopt, MSEMUopt, opt, Yopt

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

Guo, G., Sun, Y., Qian, G., & Wang, Q. (2022). LIC criterion for optimal subset selection in distributed interval estimation. Journal of Applied Statistics, 50(9), 1900-1920. doi:10.1080/02664763.2022.2053949.

Chang, D., Guo, G. (2024). LIC: An R package for optimal subset selection for distributed data. SoftwareX, 28, 101909.

Jing, G., & Guo, G. (2025). TLIC: An R package for the LIC for T distribution regression analysis. SoftwareX, 30, 102132.

Chang, D., & Guo, G. (2025). Research on Distributed Redundant Data Estimation Based on LIC. IAENG International Journal of Applied Mathematics, 55(1), 1-6.

Gao, H., & Guo, G. (2025). LIC for Distributed Skewed Regression. IAENG International Journal of Applied Mathematics, 55(9), 2925-2930.

Zhang, C., & Guo, G. (2025). The optimal subset estimation of distributed redundant data. IAENG International Journal of Applied Mathematics, 55(2), 270–277.

Jing, G., & Guo, G. (2025). Student LIC for distributed estimation. IAENG International Journal of Applied Mathematics, 55(3), 575–581.

Liu, Q., & Guo, G. (2025). Distributed estimation of redundant data. IAENG International Journal of Applied Mathematics, 55(2), 332–337.

Examples

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

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

Guo, G., Sun, Y., Qian, G., & Wang, Q. (2022). LIC criterion for optimal subset selection in distributed interval estimation. Journal of Applied Statistics, 50(9), 1900-1920. doi:10.1080/02664763.2022.2053949.

Chang, D., Guo, G. (2024). LIC: An R package for optimal subset selection for distributed data. SoftwareX, 28, 101909.

Jing, G., & Guo, G. (2025). TLIC: An R package for the LIC for T distribution regression analysis. SoftwareX, 30, 102132.

Chang, D., & Guo, G. (2025). Research on Distributed Redundant Data Estimation Based on LIC. IAENG International Journal of Applied Mathematics, 55(1), 1-6.

Gao, H., & Guo, G. (2025). LIC for Distributed Skewed Regression. IAENG International Journal of Applied Mathematics, 55(9), 2925-2930.

Zhang, C., & Guo, G. (2025). The optimal subset estimation of distributed redundant data. IAENG International Journal of Applied Mathematics, 55(2), 270–277.

Jing, G., & Guo, G. (2025). Student LIC for distributed estimation. IAENG International Journal of Applied Mathematics, 55(3), 575–581.

Liu, Q., & Guo, G. (2025). Distributed estimation of redundant data. IAENG International Journal of Applied Mathematics, 55(2), 332–337.

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)

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

Guo, G., Sun, Y., Qian, G., & Wang, Q. (2022). LIC criterion for optimal subset selection in distributed interval estimation. Journal of Applied Statistics, 50(9), 1900-1920. doi:10.1080/02664763.2022.2053949.

Chang, D., Guo, G. (2024). LIC: An R package for optimal subset selection for distributed data. SoftwareX, 28, 101909.

Jing, G., & Guo, G. (2025). TLIC: An R package for the LIC for T distribution regression analysis. SoftwareX, 30, 102132.

Chang, D., & Guo, G. (2025). Research on Distributed Redundant Data Estimation Based on LIC. IAENG International Journal of Applied Mathematics, 55(1), 1-6.

Gao, H., & Guo, G. (2025). LIC for Distributed Skewed Regression. IAENG International Journal of Applied Mathematics, 55(9), 2925-2930.

Zhang, C., & Guo, G. (2025). The optimal subset estimation of distributed redundant data. IAENG International Journal of Applied Mathematics, 55(2), 270–277.

Jing, G., & Guo, G. (2025). Student LIC for distributed estimation. IAENG International Journal of Applied Mathematics, 55(3), 575–581.

Liu, Q., & Guo, G. (2025). Distributed estimation of redundant data. IAENG International Journal of Applied Mathematics, 55(2), 332–337.

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

Guo, G., Sun, Y., Qian, G., & Wang, Q. (2022). LIC criterion for optimal subset selection in distributed interval estimation. Journal of Applied Statistics, 50(9), 1900-1920. doi:10.1080/02664763.2022.2053949.

Chang, D., Guo, G. (2024). LIC: An R package for optimal subset selection for distributed data. SoftwareX, 28, 101909.

Jing, G., & Guo, G. (2025). TLIC: An R package for the LIC for T distribution regression analysis. SoftwareX, 30, 102132.

Chang, D., & Guo, G. (2025). Research on Distributed Redundant Data Estimation Based on LIC. IAENG International Journal of Applied Mathematics, 55(1), 1-6.

Gao, H., & Guo, G. (2025). LIC for Distributed Skewed Regression. IAENG International Journal of Applied Mathematics, 55(9), 2925-2930.

Zhang, C., & Guo, G. (2025). The optimal subset estimation of distributed redundant data. IAENG International Journal of Applied Mathematics, 55(2), 270–277.

Jing, G., & Guo, G. (2025). Student LIC for distributed estimation. IAENG International Journal of Applied Mathematics, 55(3), 575–581.

Liu, Q., & Guo, G. (2025). Distributed estimation of redundant data. IAENG International Journal of Applied Mathematics, 55(2), 332–337.

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)

cerr function is used to generate a dataset where the error term follows cosine-based distributions

Description

This cerr function generates a dataset with a specified number of observations and predictors, along with a response vector that has an error term sampled from cosine-based distributions on [-pi/2, pi/2].

Usage

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

Arguments

n

is the number of observations

nr

is the number of observations with a different error distribution segment (the second block)

p

is the dimension of the observation

dist_type

is the cosine-based sampler to use: "cosine_random", "cosine_rejection_sampling", or "cosine_metropolis_hastings"

...

is additional arguments (reserved for compatibility; not used)

Value

X,Y,e

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

Guo, G., Sun, Y., Qian, G., & Wang, Q. (2022). LIC criterion for optimal subset selection in distributed interval estimation. Journal of Applied Statistics, 50(9), 1900-1920. doi:10.1080/02664763.2022.2053949.

Chang, D., Guo, G. (2024). LIC: An R package for optimal subset selection for distributed data. SoftwareX, 28, 101909.

Jing, G., & Guo, G. (2025). TLIC: An R package for the LIC for T distribution regression analysis. SoftwareX, 30, 102132.

Chang, D., & Guo, G. (2025). Research on Distributed Redundant Data Estimation Based on LIC. IAENG International Journal of Applied Mathematics, 55(1), 1-6.

Gao, H., & Guo, G. (2025). LIC for Distributed Skewed Regression. IAENG International Journal of Applied Mathematics, 55(9), 2925-2930.

Zhang, C., & Guo, G. (2025). The optimal subset estimation of distributed redundant data. IAENG International Journal of Applied Mathematics, 55(2), 270–277.

Jing, G., & Guo, G. (2025). Student LIC for distributed estimation. IAENG International Journal of Applied Mathematics, 55(3), 575–581.

Liu, Q., & Guo, G. (2025). Distributed estimation of redundant data. IAENG International Journal of Applied Mathematics, 55(2), 332–337.

Examples

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

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