High-dimensional empirical likelihood inference

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.

The original title of this paper is "High-dimensional statistical inferences with over-identification: confidence set estimation and specification test"

References in corpus (4)

• Nearly unbiased variable selection under minimax concave penalty
• Extending the scope of empirical likelihood
• A new scope of penalized empirical likelihood with high-dimensional estimating equations
• Local independence feature screening for nonparametric and semiparametric models by marginal empirical likelihood

Cited by in corpus (2)

• Testing the martingale difference hypothesis in high dimension
• Culling the herd of moments with penalized empirical likelihood