Help for package ELIC

Type:

Package

Title:

LIC for Distributed Elliptical Model

Version:

0.1.0

Date:

2025-08-16

Description:

This comprehensive toolkit for Distributed Elliptical model is designated as "ELIC" (The LIC for Distributed Elliptical Model Analysis) analysis. It is predicated on the assumption that the error term adheres to a Elliptical 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

NeedsCompilation:

Author:

Guangbao Guo [aut, cre], Xiyu Zhao [aut]

Maintainer:

Guangbao Guo <ggb11111111@163.com>

Repository:

CRAN

Config/testthat/edition:

Imports:

distr, distrEllipse,MASS

Suggests:

testthat (≥ 3.0.0), sn

Depends:

R (≥ 4.4.0)

Packaged:

2025-08-27 01:37:26 UTC; 13269

Date/Publication:

2025-09-04 14:20:33 UTC

A General Length and Information Criterion (LIC) Function

Description

This function applies the LIC method to find an optimal data subset, supporting various error term distributions like T-distribution and skewed distributions.

Usage

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

Arguments

X

A numeric design matrix.

Y

A numeric response vector.

alpha

The significance level for criterion calculation, default is 0.05.

K

The number of subsets to sample, default is 10.

nk

The sample size of each subset. If NULL (default), it's calculated as n/K.

dist_type

A character string specifying the assumed error distribution. Accepts T-distribution types (e.g., "student_t") from the original TLIC, and skewed types ("skew_normal", "skew_t", "skew_laplace") from SLIC. Note: In this implementation, the core calculation is robust and does not change based on dist_type. The parameter is kept for consistency with the original functions.

Details

The function iteratively samples subsets from the data, calculates a length criterion (L1) and an information criterion (N), and finds an optimal subset based on the intersection of the best samples from both criteria. It is a general implementation combining the logic of TLIC and SLIC.

Value

A list containing the optimal model components:

MUopt

The predicted values for the optimal subset.

Bopt

The estimated coefficients for the optimal model.

MAEMUopt

The Mean Absolute Error of the optimal model.

MSEMUopt

The Mean Squared Error of the optimal model.

opt

The indices of the optimal data subset.

Yopt

The response values of the optimal subset.

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

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

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

# Example with T-distributed error data (like TLIC)
set.seed(12)
n <- 200
p <- 5
X_t <- matrix(stats::runif(n * p), ncol = p)
beta_t <- sort(stats::runif(p, 1, 5))
e_t <- stats::rt(n, df = 5)
Y_t <- X_t %*% beta_t + e_t
result_t <- ELIC(X_t, Y_t, dist_type = "student_t")
str(result_t)

# Example with Skew-Normal error data (like SLIC)
if (requireNamespace("sn", quietly = TRUE)) {
  set.seed(123)
  n <- 200
  p <- 5
  X_s <- matrix(stats::rnorm(n * p), ncol = p)
  beta_s <- stats::runif(p, 1, 2)
  e_s <- sn::rsn(n = n, xi = 0, omega = 1, alpha = 5)
  Y_s <- X_s %*% beta_s + e_s
  result_s <- ELIC(X_s, Y_s, K = 5, dist_type = "skew_normal")
  str(result_s)
}

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.