Optimal goodness-of-fit tests for normality against skewness and kurtosis alternatives
type: Item
instance of: scholarly article
title: Optimal goodness-of-fit tests for normality against skewness and kurtosis alternatives
zbMATH Open document ID: 0586.62030
DOI: 10.1016/0378-3758(86)90120-5
published in: Journal of Statistical Planning and Inference
publication date: 1986-01-01T00:00:00Z
review text: Three test statistics for the composite goodness-of-fit hypothesis of normality are presented. The proposed statistics are sums of squared L- statistics, and under the null hypothesis converge in distribution to chi-squared random variables. Further, the test procedures are asymptotically optimal for sequences of local skewness and/or kurtic alternative to the null hypothesis. The results of a simulation study indicate that the asymptotic critical values for the test procedures provide a useful approximation in samples as small as 25, and that the procedures compare favorably to existing tests in small samples.
Mathematics Subject Classification ID: 62F03
Mathematics Subject Classification ID: 62F05
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 3940415
zbMATH Keywords: kurtosis
zbMATH Keywords: asymptotic power
zbMATH Keywords: order statistics
zbMATH Keywords: composite goodness-of-fit hypothesis of normality
zbMATH Keywords: sums of squared L-statistics
zbMATH Keywords: chi-squared random variables
zbMATH Keywords: asymptotically optimal
zbMATH Keywords: skewness
zbMATH Keywords: simulation study
zbMATH Keywords: small samples
author: Vincent N. La Riccia
MaRDI profile type: Publication
full work available at URL: 0378-3758(86)90120-5
OpenAlex ID: W2021173610
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description: scientific article; zbMATH DE number 3940415