Asymptotic Deficiencies of One-Sample Rank Tests Under Restricted Adaptation

Willem/Wim Albers

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    Abstract

    In this paper we consider adaptive one-sample rank tests of the following type: the score function $J$ of the test is estimated from the sample under the restriction that $J \in \mathscr{J}$, for some given one-parameter family $\mathscr{J} = \{J_r, r \in I \subset R^1\}$. Using deficiencies, we compare the performance of such tests to that of rank tests with fixed scores. Conditions on the estimator $S$ of the parameter $r$ and on $J_r$ are given, under which the deficiency tends to a finite limit, which is obtained. For a particular class of estimators which are related to the sample kurtosis, explicit results are obtained.
    Original languageEnglish
    Pages (from-to)944-954
    JournalAnnals of statistics
    Volume7
    Issue number5
    DOIs
    Publication statusPublished - 1979

    Keywords

    • Adaptation
    • IR-70388
    • Deficiency
    • asymptotic expansions
    • contiguous alternatives
    • one-sample rank tests

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