High dimensional generalized empirical likelihood for moment restrictions with dependent data

TL;DR

This paper develops high-dimensional generalized empirical likelihood methods for dependent data, establishing consistency, asymptotic normality, and chi-square behavior, along with tests and penalized estimation for sparse models.

Contribution

It introduces a framework for GEL estimation with diverging dimensions and dependent data, including asymptotic properties, over-identification tests, and sparsity-aware penalized methods.

Findings

GEL estimator is consistent and asymptotically normal in high dimensions.

GEL ratio behaves like a chi-square distribution even with dependent data.

Proposes a penalized GEL method for sparse high-dimensional models.

Abstract

This paper considers the maximum generalized empirical likelihood (GEL) estimation and inference on parameters identified by high dimensional moment restrictions with weakly dependent data when the dimensions of the moment restrictions and the parameters diverge along with the sample size. The consistency with rates and the asymptotic normality of the GEL estimator are obtained by properly restricting the growth rates of the dimensions of the parameters and the moment restrictions, as well as the degree of data dependence. It is shown that even in the high dimensional time series setting, the GEL ratio can still behave like a chi-square random variable asymptotically. A consistent test for the over-identification is proposed. A penalized GEL method is also provided for estimation under sparsity setting.