A truncated Cramér–von Mises test of normality

Juan Kalemkerian

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 16, 3956-3975

Abstract: A new test of normality with unknown parameters is proposed in this article. We introduce a Cramér–von Mises type statistic with weight function equal to the inverse of the standard normal density function supported in the interval [−an,an] depending on the sample size n. The sequence {an} is chosen so that the statistic goes to infinity and after subtracting the mean, a suitable test statistic is obtained, with the same asymptotic law as the well-known Shapiro–Wilk statistic. It is shown that the performance of the new test in many cases improves that of other well-known tests of normality.

Date: 2019
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DOI: 10.1080/03610926.2018.1465093

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