Testing semiparametric model-equivalence hypotheses based on the characteristic function

TL;DR

This paper introduces three new statistical tests for multivariate data to assess symmetry, homogeneity, and independence by comparing characteristic functions, with analysis of their asymptotic properties and finite-sample performance.

Contribution

It presents novel weighted-distance-based test criteria for semiparametric model-equivalence hypotheses involving characteristic functions.

Findings

Tests are computationally convenient with proper weight functions.

Asymptotic properties of the tests are thoroughly analyzed.

Numerical studies demonstrate good finite-sample performance.

Abstract

We propose three test criteria each of which is appropriate for testing, respectively, the equivalence hypotheses of symmetry, of homogeneity, and of independence, with multivariate data. All quantities have the common feature of involving weighted--type distances between characteristic functions and are convenient from the computational point of view if the weight function is properly chosen. The asymptotic behavior of the tests under the null hypothesis is investigated, and numerical studies are conducted in order to examine the performance of the criteria in finite samples.