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Bibliographic Details
Main Author: Stepanov, Alexei
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2506.06056
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author Stepanov, Alexei
author_facet Stepanov, Alexei
contents In the present paper, we propose a new rank correlation coefficient $r_n$, which is a sample analogue of the theoretical correlation coefficient $r$, which, in turn, was proposed in the recent work of Stepanov (2025b). We discuss the properties of $r_n$ and compare $r_n$ with known rank Spearman $ρ_{S,n}$, Kendall $τ_n$ and sample Pearson $ρ_n$ correlation coefficients. Simulation experiments show that when the relationship between $X$ and $Y$ is not close to linear, $r_n$ performs better than other correlation coefficients. We also find analytically the values of $Var(τ_n)$ and $Var(r_n)$. This allows to estimate theoretically the asymptotic performance of $τ_n$ and $r_n$.
format Preprint
id arxiv_https___arxiv_org_abs_2506_06056
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On Rank Correlation Coefficients
Stepanov, Alexei
Statistics Theory
G.3
G.3
In the present paper, we propose a new rank correlation coefficient $r_n$, which is a sample analogue of the theoretical correlation coefficient $r$, which, in turn, was proposed in the recent work of Stepanov (2025b). We discuss the properties of $r_n$ and compare $r_n$ with known rank Spearman $ρ_{S,n}$, Kendall $τ_n$ and sample Pearson $ρ_n$ correlation coefficients. Simulation experiments show that when the relationship between $X$ and $Y$ is not close to linear, $r_n$ performs better than other correlation coefficients. We also find analytically the values of $Var(τ_n)$ and $Var(r_n)$. This allows to estimate theoretically the asymptotic performance of $τ_n$ and $r_n$.
title On Rank Correlation Coefficients
topic Statistics Theory
G.3
G.3
url https://arxiv.org/abs/2506.06056