Skewness and kurtosis as locally best invariant tests of normality

Details Skewness and kurtosis as locally best invariant tests of normality Skewness and kurtosis as locally best invariant tests of normality

2006-08-20

arxiv.org/abs/math/0608499v1

Mathematics

Statistics Theory

Scientific paper

Consider testing normality against a one-parameter family of univariate distributions containing the normal distribution as the boundary, e.g., the family of $t$-distributions or an infinitely divisible family with finite variance. We prove that under mild regularity conditions, the sample skewness is the locally best invariant (LBI) test of normality against a wide class of asymmetric families and the kurtosis is the LBI test against symmetric families. We also discuss non-regular cases such as testing normality against the stable family and some related results in the multivariate cases.

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