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Some asymptotic distributions in the location-scale model

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Summary

Scale and location estimators defined by the equation

$$\sum\limits_{i = 1}^n {J[{i \mathord{\left/ {\vphantom {i {(n + 1)}}} \right. \kern-\nulldelimiterspace} {(n + 1)}}]\psi [{{(X_{(i)} - \hat T_n )} \mathord{\left/ {\vphantom {{(X_{(i)} - \hat T_n )} {\hat V_n }}} \right. \kern-\nulldelimiterspace} {\hat V_n }}] = 0} $$

are introduced. Their asymptotic distribution is derived. If the underlying distribution is known, a large number of estimators is shown to be efficient. Step versions of these estimators are also studied. Hampel's (1974,J. Amer. Statist. Ass.,69, 383–393), concept of influence curve is used. All the asymptotic results presented in this paper are derived from a general theorem of Rivest (1979,Tech. Rep., Univ. of Toronto).

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Authors and Affiliations

  1. Université Laval, Laval, Canada

    Louis-Paul Rivest

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  1. Louis-Paul Rivest
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Rivest, LP. Some asymptotic distributions in the location-scale model. Ann Inst Stat Math 34, 225–239 (1982). https://doi.org/10.1007/BF02481024

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  • DOI: https://doi.org/10.1007/BF02481024

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