A Score Test against One-Sided Alternatives

Abstract A score-type statistic, T s , is introduced for testing H: ψ = 0 against K: ψ ≥ 0 and more general one-sided hypotheses when nuisance parameters may be present; ψ is a vector parameter. The main advantages of T s , are that it requires estimation of the model only under the null hypothesis and that, it is asymptotically equivalent to the likelihood ratio statistic; these are precisely the reasons for the popularity of the score tests for testing against two-sided alternatives. In this sense, T s preserves the main attractive features of the classical two-sided score test. The theoretical results are presented in a general framework where the likelihood-based score function is replaced by an estimating function so that the test is applicable even if the exact population distribution is unknown. Computation of T s , is simplified by the fact that it can be computed easily once the corresponding two-sided statistic has been computed. The relevance and simplicity of T s are illustrated by discussing ...

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