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

Michael Browne () and Alexander Shapiro

Psychometrika, 2015, vol. 80, issue 1, 196-199

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. Copyright The Psychometric Society 2015

Keywords: covariance structures; statistical test; asymptotics (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11336-013-9383-8

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