An extension of the Plancherel measure

TL;DR

This paper introduces an extension of the Plancherel measure to test the iid hypothesis for samples in the unit square, discusses its asymptotic properties, and compares the power of various tests using permutation models.

Contribution

It extends the classical Plancherel measure framework to new settings and analyzes the asymptotic behavior relevant for hypothesis testing.

Findings

Extension of Plancherel measure for iid testing

Asymptotic analysis of the extended measure

Comparison of test powers in permutation models

Abstract

Given a distribution in the unite square and having iid sample from it the first question what a statistician might do to test the hypothesis that the sample is iid. For this purpose an extension of the Plancherel measure is introduced. Recent literature on asymptotic behavior of Plancherel measure is discussed with extension to the new set up. Models for random permutations are described and the power of different tests is compared.