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December, 1986 Asymptotic Distribution of the Shapiro-Wilk $W$ for Testing for Normality
J. R. Leslie, M. A. Stephens, S. Fotopoulos
Ann. Statist. 14(4): 1497-1506 (December, 1986). DOI: 10.1214/aos/1176350172

Abstract

Twenty years have elapsed since the Shapiro-Wilk statistic $W$ for testing the normality of a sample first appeared. In that time a number of statistics that are close relatives of $W$ have been found to have a common (known) asymptotic distribution. It was assumed, therefore, that $W$ must have that asymptotic distribution. We show this to be the case and examine the norming constants that are used with all the statistics. In addition the consistency of the $W$ test is established.

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J. R. Leslie. M. A. Stephens. S. Fotopoulos. "Asymptotic Distribution of the Shapiro-Wilk $W$ for Testing for Normality." Ann. Statist. 14 (4) 1497 - 1506, December, 1986. https://doi.org/10.1214/aos/1176350172

Information

Published: December, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0622.62019
MathSciNet: MR868314
Digital Object Identifier: 10.1214/aos/1176350172

Subjects:
Primary: 62F05
Secondary: 62E20, 62G30

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 4 • December, 1986
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