A new nonparametric method for variance estimation and confidence interval construction for Spearman's rank correlation.
type: Item
instance of: scholarly article
title: A new nonparametric method for variance estimation and confidence interval construction for Spearman's rank correlation.
zbMATH Open document ID: 1043.62021
DOI: 10.1016/S0167-9473(99)00077-8
published in: Computational Statistics and Data Analysis
publication date: 2000-10-26T00:00:00Z
review text: Spearman's rank correlation, \(\rho_{s}\), has become one of the most widely used nonparametric statistical techniques. However, explicit formulas for the finite sample variance of its point estimate, \(\widehat\rho_{s}\), are generally not available, except under special conditions, and the estimation of this variance from observed data remains a challenging statistical problem. We show that \(\widehat\rho_{s}\) can be calculated from a two-way contingency table with categories defined by the bivariate ranks. We note that this table has the ``empirical bivariate quantile-partitioned'' (EBQP) distribution [the author et al., Biometrics 53, 1054--1069 (1997; Zbl 0896.62114)], and hence \(\widehat\rho_{s}\) belongs to the class of statistics with distributions derived from the EBQP distribution. The study of \(\widehat\rho_{s}\) provides an opportunity to extend large sample EBQP methods to handle the special challenges posed by statistics calculated from EBQP tables defined by bivariate ranks. We present extensive simulations to study the estimation of the sample variance of \(\widehat\rho_{s}\) and the coverage of confidence intervals for this measure. We compare these results for the EBQP method with those for the bootstrap and jackknife algorithms. We illustrate the use of these nonparametric methods on two data sets, Spearman's original data set and an example from nutritional epidemiology. These results demonstrate that standard EBQP methods can be successfully adapted for the estimation of the sample variance of \(\widehat\rho_{s}\). They also suggest that EBQP methods should be used to estimate the sample variances of other nonparametric statistics calculated from bivariate ranks, such as Kendall's tau.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62H17
Mathematics Subject Classification ID: 62G15
Mathematics Subject Classification ID: 62H20
zbMATH DE Number: 1521635
zbMATH Keywords: Bootstrap
zbMATH Keywords: empirical bivariate quantile-partitioned (EBQP) distribution
zbMATH Keywords: jackknife
zbMATH Keywords: nonparametric statistics
zbMATH Keywords: Spearman's rank correlation
author: Craig B. Borkowf
describes a project that uses: GAUSS
describes a project that uses: bootstrap
MaRDI profile type: Publication
cites work: Q4098510
cites work: Analyzing Bivariate Continuous Data Grouped into Categories Defined by Empirical Quantiles of Marginal Distributions
cites work: The variance of Spearman's rho in normal samples
cites work: Q4318617
cites work: TESTS FOR RANK CORRELATION COEFFICIENTS. I
cites work: Q5661032
cites work: The Non-Null Distribution of the Spearman Rank Correlation Coefficient
cites work: Q3999009
cites work: Some Concepts of Dependence
cites work: Q4125587
cites work: Q3219581
cites work: Nonparametric Statistical Data Modeling
cites work: Q3938370
cites work: Q5819797
Wikidata QID: Q127018444
description: scientific article; zbMATH DE number 1521635