Two-dimensional Kolmogorov-type Goodness-of-fit Tests Based on Characterizations and their Asymptotic Efficiencies

TL;DR

This paper introduces new two-dimensional goodness-of-fit tests based on novel characterizations, including independence-based characterization, and analyzes their asymptotic properties and efficiencies.

Contribution

It presents the first use of independence-based characterization for goodness-of-fit testing and extends large deviation theorems to multidimensional cases.

Findings

New supremum-type tests proposed for 2D goodness-of-fit

Asymptotic behaviors of the tests are analyzed

Bahadur efficiencies against close alternatives are calculated

Abstract

In this paper new two-dimensional goodness of fit tests are proposed. They are of supremum-type and are based on different types of characterizations. For the first time a characterization based on independence of two statistics is used for goodness-of-fit testing. The asymptotics of the statistics is studied and Bahadur efficiencies of the tests against some close alternatives are calculated. In the process a theorem on large deviations of Kolmogorov-type statistics has been extended to the multidimensional case.