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Hypothesis testing when a nuisance parameter is present only under the alternative
干扰参数仅在备择假设下存在时的假设检验
We wish to test a simple hypothesis against a family of alternatives indexed by a one-dimensional parameter, θ. We use a test derived from the corresponding family of test statistics appropriate for the case when θ is given. Davies (1977) introduced this problem when these test statistics had normal distributions. The present paper considers the case when their distribution is chi-squared. The results are applied to the detection of a discrete frequency component of unknown…
Rank Tests for “Lehmann's Alternative”
针对 Lehmann 备择的秩检验
Large and small sample properties of tests introduced by Lehmann and Savage for the two-sample problem are examined under Lehmann's alternative.
Rank Tests for "Lehmann's Alternative"
Beta-Optimal Tests and an Application to the Summary Evaluation of Experiments
β 最优检验及其在实验综合评价中的应用
Summary A concept of optimality of a test, based on the speed with which its power function reaches a pre-assigned value, is introduced and conditions for a test to have this property are considered. The concept is applied to the weighted combination of independent normal test statistics; tests for the presence of effects and for the equality of effects are deduced.