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Biometrika 1983 70(2):401-409; doi:10.1093/biomet/70.2.401
© 1983 by Biometrika Trust
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Diagnostic tests of distributional shape

D. J. SPIEGELHALTER

MRC Biostatistics Unit Cambridge

Summary

Many statistical procedures are, strictly speaking, only appropriate when a simplifying assumption about the shape of an error distribution is made, and such an assumption may need to be checked against departures in specific parametric directions. A number of ‘diagnostic’ test procedures are summarized in which location and scale may be unknown, and examples are given in the context of testing for an exponential or Gaussian shape. Approximate efficient scores are emphasized which lead to both well known and novel test statistics. In particular, we show that the standard measures of skewness and kurtosis are asymptotically locally optimal test statistics for normality against departures in the log gamma and Student t family respectively. The properties of two new test statistics are briefly investigated.

Key Words: Efficient score • Locally more powerful • Test for normality


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