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A Nonparametric Test of Missing Completely at Random for Incomplete Multivariate Data

Published online by Cambridge University Press:  01 January 2025

Jun Li  and
Yao Yu
Jun Li*
Affiliation:
University of California, Riverside
Yao Yu
Affiliation:
University of California, Riverside
*
Correspondence should be sent to Jun Li, Department of Statistics, University of California, Riverside, Riverside, CA 92521, USA. E-mail: jun.li@ucr.edu
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Abstract

Missing data occur in many real world studies. Knowing the type of missing mechanisms is important for adopting appropriate statistical analysis procedure. Many statistical methods assume missing completely at random (MCAR) due to its simplicity. Therefore, it is necessary to test whether this assumption is satisfied before applying those procedures. In the literature, most of the procedures for testing MCAR were developed under normality assumption which is sometimes difficult to justify in practice. In this paper, we propose a nonparametric test of MCAR for incomplete multivariate data which does not require distributional assumptions. The proposed test is carried out by comparing the distributions of the observed data across different missing-pattern groups. We prove that the proposed test is consistent against any distributional differences in the observed data. Simulation shows that the proposed procedure has the Type I error well controlled at the nominal level for testing MCAR and also has good power against a variety of non-MCAR alternatives.

Keywords

missing datamissing completely at randomnonparametric test
Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 3 , September 2015 , pp. 707 - 726
Copyright
Copyright © 2014 The Psychometric Society

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