How to Build Optimal Tests for Normality Under Possibly Singular Fisher Information

Andreas Anastasiou () and Christophe Ley ()
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Andreas Anastasiou: University of Cyprus
Christophe Ley: University of Luxembourg

A chapter in Recent Advances in Econometrics and Statistics, 2024, pp 149-166 from Springer

Abstract: Abstract In this chapter, we show how to construct efficient tests for normality against generalized skew-normal distributions, which contain the most popular skew alternative, namely, the skew-normal distribution. This task is highly nontrivial due to the fact that the Fisher information matrix for location and skewness is singular in the vicinity of symmetry. Thanks to a reparametrization proposed in a paper by Marc Hallin with the second author, we are able to develop the usual Le Cam methodology for this peculiar model and hence derive optimal tests for normality, hereby shedding new light on some well-known tests from the literature.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-61853-6_8

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DOI: 10.1007/978-3-031-61853-6_8

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