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Comment on the Asymptotics of a Distribution-Free Goodness of Fit Test Statistic

Published online by Cambridge University Press:  01 January 2025

Michael W. Browne  and
Alexander Shapiro
Michael W. Browne*
Affiliation:
Ohio State University
Alexander Shapiro
Affiliation:
Georgia Institute of Technology
*
Requests for reprints should be sent to Michael W. Browne, Department of Psychology, The Ohio State University, 1835 Neil Avenue, Columbus, OH 43210-1222, USA. E-mail: browne.4@osu.edu
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Abstract

In a recent article Jennrich and Satorra (Psychometrika 78: 545–552, 2013) showed that a proof by Browne (British Journal of Mathematical and Statistical Psychology 37: 62–83, 1984) of the asymptotic distribution of a goodness of fit test statistic is incomplete because it fails to prove that the orthogonal component function employed is continuous. Jennrich and Satorra (Psychometrika 78: 545–552, 2013) showed how Browne’s proof can be completed satisfactorily but this required the development of an extensive and mathematically sophisticated framework for continuous orthogonal component functions. This short note provides a simple proof of the asymptotic distribution of Browne’s (British Journal of Mathematical and Statistical Psychology 37: 62–83, 1984) test statistic by using an equivalent form of the statistic that does not involve orthogonal component functions and consequently avoids all complicating issues associated with them.

Keywords

covariance structuresstatistical testasymptotics
Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 1 , March 2015 , pp. 196 - 199
Copyright
Copyright © 2013 The Psychometric Society

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References

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