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Main Author: Stepanov, Alexei
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2603.25055
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author Stepanov, Alexei
author_facet Stepanov, Alexei
contents In the present paper, we discuss for the first time the theoretical Kendall correlation coefficient for non-identical bivariate data. In the non-identical case, we first introduce a theoretical Kendall correlation coefficient $τ_n$ and show that the expected value of the rank Kendall correlation coefficient $\tildeτ_n$ is equal to $τ_n$. We then prove that $\tildeτ_n$ converges in probability to $τ=\lim_{n\rightarrow\infty} τ_n$. These facts enable us to state that $τ_n$ is a correctly defined theoretical Kendall correlation coefficient for the non-identical case. We also support our theoretical results by simulation experiments.
format Preprint
id arxiv_https___arxiv_org_abs_2603_25055
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Kendall Correlation Coefficient for non-Identically Distributed Variables
Stepanov, Alexei
Statistics Theory
In the present paper, we discuss for the first time the theoretical Kendall correlation coefficient for non-identical bivariate data. In the non-identical case, we first introduce a theoretical Kendall correlation coefficient $τ_n$ and show that the expected value of the rank Kendall correlation coefficient $\tildeτ_n$ is equal to $τ_n$. We then prove that $\tildeτ_n$ converges in probability to $τ=\lim_{n\rightarrow\infty} τ_n$. These facts enable us to state that $τ_n$ is a correctly defined theoretical Kendall correlation coefficient for the non-identical case. We also support our theoretical results by simulation experiments.
title Kendall Correlation Coefficient for non-Identically Distributed Variables
topic Statistics Theory
url https://arxiv.org/abs/2603.25055