Asymptotic Inference for Rank Correlations

TL;DR

This paper develops comprehensive asymptotic inference methods for various rank correlations, including variance estimation and confidence intervals, applicable to both iid and time series data, addressing gaps in existing theory.

Contribution

It introduces new asymptotic distributions and consistent variance estimators for classical rank correlations, extending results to discrete variables and time series.

Findings

Provides asymptotic distributions for rank correlations in iid and time series data.

Develops consistent variance estimators enabling confidence intervals and hypothesis tests.

Demonstrates finite-sample performance and practical applications through simulations and case studies.

Abstract

Kendall's tau and Spearman's rho are widely used tools for measuring dependence. Surprisingly, when it comes to asymptotic inference for these rank correlations, some fundamental results and methods have not yet been developed, in particular for discrete random variables and in the time series case, and concerning variance estimation in general. Consequently, asymptotic confidence intervals are not available. We provide a comprehensive treatment of asymptotic inference for classical rank correlations, including Kendall's tau, Spearman's rho, Goodman-Kruskal's gamma, Kendall's tau-b, and grade correlation. We derive asymptotic distributions for both iid and time series data, resorting to asymptotic results for U-statistics, and introduce consistent variance estimators. This enables the construction of confidence intervals and tests, generalizes classical results for continuous random variables and leads to corrected versions of widely used tests of independence. We analyze the finite-sample performance of our variance estimators, confidence intervals, and tests in simulations and illustrate their use in case studies.