A penalized empirical likelihood method in high dimensions

TL;DR

This paper introduces a penalized empirical likelihood method for high-dimensional inference on the population mean, accommodating various dependence structures and providing a unified calibration approach validated through simulations.

Contribution

It develops a novel penalized empirical likelihood framework for high-dimensional data with dependence, deriving its asymptotic distributions and proposing a universal subsampling calibration.

Findings

Asymptotic distributions vary with dependence structure

Unified subsampling calibration is valid across scenarios

Finite sample performance is demonstrated via simulations

Abstract

This paper formulates a penalized empirical likelihood (PEL) method for inference on the population mean when the dimension of the observations may grow faster than the sample size. Asymptotic distributions of the PEL ratio statistic is derived under different component-wise dependence structures of the observations, namely, (i) non-Ergodic, (ii) long-range dependence and (iii) short-range dependence. It follows that the limit distribution of the proposed PEL ratio statistic can vary widely depending on the correlation structure, and it is typically different from the usual chi-squared limit of the empirical likelihood ratio statistic in the fixed and finite dimensional case. A unified subsampling based calibration is proposed, and its validity is established in all three cases, (i)-(iii). Finite sample properties of the method are investigated through a simulation study.