Minimum Kernel Discrepancy Estimators

TL;DR

This paper reviews minimum kernel discrepancy estimators, discussing their use in statistical model selection and providing a general theoretical framework for their asymptotic properties.

Contribution

It introduces a comprehensive theoretical framework for analyzing the asymptotic behavior of minimum kernel discrepancy estimators in statistics.

Findings

Reviewed the application of kernel discrepancies in statistical model selection

Established asymptotic properties of minimum kernel discrepancy estimators

Connected kernel methods with statistical inference

Abstract

For two decades, reproducing kernels and their associated discrepancies have facilitated elegant theoretical analyses in the setting of quasi Monte Carlo. These same tools are now receiving interest in statistics and related fields, as criteria that can be used to select an appropriate statistical model for a given dataset. The focus of this article is on minimum kernel discrepancy estimators, whose use in statistical applications is reviewed, and a general theoretical framework for establishing their asymptotic properties is presented.