Exponentially tilted likelihood inference on growing dimensional unconditional moment models

TL;DR

This paper introduces a penalized exponentially tilted likelihood method for variable selection and estimation in high-dimensional unconditional moment models, demonstrating robustness and strong theoretical properties.

Contribution

It proposes a novel PETL approach tailored for growing-dimensional models with correlation and misspecification, with proven consistency and asymptotic properties.

Findings

PETL estimators are consistent and possess oracle properties.

The PETL ratio statistic asymptotically follows a chi-squared distribution.

Simulation studies confirm the method's finite-sample performance.

Abstract

Growing-dimensional data with likelihood unavailable are often encountered in various fields. This paper presents a penalized exponentially tilted likelihood (PETL) for variable selection and parameter estimation for growing dimensional unconditional moment models in the presence of correlation among variables and model misspecifica- tion. Under some regularity conditions, we investigate the consistent and oracle proper- ties of the PETL estimators of parameters, and show that the constrainedly PETL ratio statistic for testing contrast hypothesis asymptotically follows the central chi-squared distribution. Theoretical results reveal that the PETL approach is robust to model mis- specification. We also study high-order asymptotic properties of the proposed PETL estimators. Simulation studies are conducted to investigate the finite performance of the proposed methodologies. An example from the Boston Housing Study is illustrated.