Measures of lack of fit from tests of chi-squared type
type: Item
instance of: scholarly article
title: Measures of lack of fit from tests of chi-squared type
zbMATH Open document ID: 0598.62042
DOI: 10.1016/0378-3758(84)90067-3
author: David S. Moore
published in: Journal of Statistical Planning and Inference
publication date: 1984-01-01T00:00:00Z
review text: If \(X^ 2\) is the Pearson chi-squared statistic for testing fit, then \(X^ 2/n\) has long been considered an associated measure of the degree of lack of fit. Here we consider two classes of statistics of chi-squared type, each having \(X^ 2\) as a member. The first is a class of directed divergence statistics discussed by \textit{N. Cressie} and \textit{T. R. C. Read} [J. R. Stat. Soc., Ser. B 46, 440-464 (1984; Zbl 0571.62017)], the second consists of nonnegative definite quadratic forms in the standardized cell frequencies. We investigate the large sample behavior of T/n, where T is any of these statistics. A number of auxiliary results on the Cressie-Read statistics are also obtained. The measures are illustrated by application to data from classical physics compiled by \textit{S. M. Stigler} [Ann. Stat. 5, 1055-1098 (1977; Zbl 0374.62050)].
Mathematics Subject Classification ID: 62G10
zbMATH DE Number: 3965198
zbMATH Keywords: goodness of fit
zbMATH Keywords: minimum discrepancy estimators
zbMATH Keywords: Pearson chi-squared statistic
zbMATH Keywords: degree of lack of fit
zbMATH Keywords: directed divergence statistics
zbMATH Keywords: nonnegative definite quadratic forms
zbMATH Keywords: large sample behavior
zbMATH Keywords: Cressie-Read statistics
MaRDI profile type: Publication
full work available at URL: 0378-3758(84)90067-3
OpenAlex ID: W2088184861
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description: scientific article; zbMATH DE number 3965198