High-dimensional empirical likelihood inference

TL;DR

This paper develops new empirical likelihood methods for high-dimensional inference, enabling valid confidence sets and model tests despite the challenges posed by large parameter spaces and growing data dimensions.

Contribution

It introduces a novel construction of estimating equations that reduces nuisance parameter impact, facilitating high-dimensional confidence regions and model specification tests.

Findings

Valid confidence regions for high-dimensional parameters

Effective model specification testing using empirical likelihood ratios

Numerical studies show promising performance of the methods

Abstract

High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters, and model specifications test. For the first one, we propose to construct a new set of estimating equations such that the impact from estimating the high-dimensional nuisance parameters becomes asymptotically negligible. The new construction enables us to estimate a valid confidence region by empirical likelihood ratio. For the second one, we propose a test statistic as the maximum of the marginal empirical likelihood ratios to quantify data evidence against the model specification. Our theory establishes the validity of the proposed empirical likelihood approaches, accommodating over-identification and exponentially growing data dimensionality. The numerical studies demonstrate promising performance and potential practical benefits of the new methods.