Nonparametric Analysis of Clustered Multivariate Data

by   Jaakko Nevalainen, et al.

There has been a wide interest to extend univariate and multivariate nonparametric procedures to clustered and hierarchical data. Traditionally, parametric mixed models have been used to account for the correlation structures among the dependent observational units. In this work we extend multivariate nonparametric procedures for one-sample and several samples location problems to clustered data settings. The results are given for a general score function, but with an emphasis on spatial sign and rank methods. Mixed models notation involving design matrices for fixed and random effects is used throughout. The asymptotic variance formulas and limiting distributions of the test statistics under the null hypothesis and under a sequence of alternatives are derived, as well as the limiting distributions for the corresponding estimates. The approach based on a general score function also shows, for example, how M-estimates behave with clustered data. Efficiency studies demonstrate practical advantages and disadvantages of the use of spatial sign and rank scores, and their weighted versions. Small sample procedures based on sign change and permutation principles are discussed. Further development of nonparametric methods for cluster correlated data would benefit from the notation already familiar to statisticians working under normality assumptions.


page 1

page 2

page 3

page 4


Multivariate Rank-based Distribution-free Nonparametric Testing using Measure Transportation

In this paper, we propose a general framework for distribution-free nonp...

Center-Outward Sign- and Rank-Based Quadrant, Spearman, and Kendall Tests for Multivariate Independence

Defining multivariate generalizations of the classical univariate ranks ...

Rank Intraclass Correlation for Clustered Data

Clustered data are common in biomedical research. Observations in the sa...

Nonparametric MANOVA in Mann-Whitney effects

Multivariate analysis of variance (MANOVA) is a powerful and versatile m...

Nonparametric Method for Clustered Data in Pre-Post Factorial Design

In repeated measures factorial designs involving clustered units, parame...

The Asymptotic Properties of the One-Sample Spatial Rank Methods

For a set of p-variate data points y_1,…, y_n, there are several version...

Please sign up or login with your details

Forgot password? Click here to reset