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Biometrika 1986 73(2):437-446; doi:10.1093/biomet/73.2.437
© 1986 by Biometrika Trust
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Neyman-type smooth tests for location-scale families

J. C. W. RAYNER1 and D. J. BEST2

1Department of Mathematics and Statistics, University of Otago Dunedin, New Zealand
2CSIRO, Division of Mathematics and Statistics North Ryde, N.S.W. 2113, Australia

The smooth tests of Neyman (1937) are modified to permit composite alternatives and a choice of orthonormal functions in their construction. These orthonormal functions may be chosen to improve detection of particular alternatives. The tests are easy to apply and have useful orthogonal components. A test for exponentiality is examined, and shown to perform well against its competitors.

Key Words: Complete orthonormal basis • Power • Simple and composite hypothesis • Smooth goodness-of-fit test • Test for exponentiality


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