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INVARIANT HYPOTHESIS TESTING IN ORDER-RESTRICTED INFERENCE

H.W. Peers
Brazilian Journal of Probability and Statistics
Vol. 9, No. 2 (NOVEMBER 1995), pp. 99-118
Stable URL: http://www.jstor.org/stable/43601453
Page Count: 20
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INVARIANT HYPOTHESIS TESTING IN ORDER-RESTRICTED INFERENCE
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Abstract

The construction by suitable algorithms of isotonised maximum likelihood estimators and associated likelihood ratio tests is considered in an arbitrary parametric framework. An approximate X̅² statistic for testing order-restricted hypotheses is introduced, and its asymptotic invariance properties discussed under change of parameter. The degree of parameter-dependence is examined numerically on data from astronomy modelled by a Pareto distribution. A suggestion is made for a judicious choice of basic parameter to promote agreement with a well-established X̅² test on normal means.

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