Work

Statistical Inference for High-Dimensional Heteroscedastic Partially Single-Index Models

Year: 2025

Type: article

Abstract: In this study, we propose a novel penalized empirical likelihood approach that simultaneously performs parameter estimation and variable selection in heteroscedastic partially linear single-index models with a diverging number of parameters. It is rigorously proved that the proposed method possesses the oracle property: (i) with probability tending to 1, the zero components are consistently estimated as zero; (ii) the estimators for nonzero coefficients achieve asymptotic efficiency. Furthermore, the penalized empirical log-likelihood ratio statistic is shown to asymptotically follow a standard chi-squared distribution under the null hypothesis. This methodology can be naturally applied to pure partially linear models and single-index models in high-dimensional settings. Simulation studies and real-world data analysis are conducted to examine the properties of the presented approach.

Source: Entropy

DOI: 10.3390/e27090964

Authors: Jianglin Fang, Zhikun Tian

Institution: Hunan Institute of Engineering

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Scientific Research Foundation of Hunan Provincial Education Department