The Annals of Statistics

The Asymptotic Equivalence of Some Modified Shapiro-Wilk Statistics-- Complete and Censored Sample Cases

Steve Verrill and Richard A. Johnson

Full-text: Open access

Abstract

The Shapiro-Wilk statistic and its modifications are widely applied in tests for normality. We establish the asymptotic equivalence of a class of statistics based on different choices of normal scores. In particular, we conclude that the Shapiro-Francia, Filliben, Weisberg-Bingham and de Wet-Venter versions of the statistic are asymptotically equivalent. Our results also apply to the Type I and Type II censored data cases.

Article information

Source
Ann. Statist., Volume 15, Number 1 (1987), 413-419.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350275

Digital Object Identifier
doi:10.1214/aos/1176350275

Mathematical Reviews number (MathSciNet)
MR885746

Zentralblatt MATH identifier
0656.62066

JSTOR
links.jstor.org

Subjects
Primary: 62F99: None of the above, but in this section
Secondary: 62E20: Asymptotic distribution theory 62G99: None of the above, but in this section

Keywords
Correlation tests of normality modified Shapiro-Wilk statistics Shapiro-Francia statistic asymptotic equivalence Type I censoring Type II censoring

Citation

Verrill, Steve; Johnson, Richard A. The Asymptotic Equivalence of Some Modified Shapiro-Wilk Statistics-- Complete and Censored Sample Cases. Ann. Statist. 15 (1987), no. 1, 413--419. doi:10.1214/aos/1176350275. https://projecteuclid.org/euclid.aos/1176350275


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