The Annals of Statistics
- Ann. Statist.
- Volume 14, Number 4 (1986), 1497-1506.
Asymptotic Distribution of the Shapiro-Wilk $W$ for Testing for Normality
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.
Ann. Statist., Volume 14, Number 4 (1986), 1497-1506.
First available in Project Euclid: 12 April 2007
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Leslie, J. R.; Stephens, M. A.; Fotopoulos, S. Asymptotic Distribution of the Shapiro-Wilk $W$ for Testing for Normality. Ann. Statist. 14 (1986), no. 4, 1497--1506. doi:10.1214/aos/1176350172. https://projecteuclid.org/euclid.aos/1176350172