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A new family of omega-square-type statistics with Bahadur local optimality for the location family of generalized logistic distributions

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  • Pycke, Jean-Renaud

Abstract

We introduce a family of weighted omega-square statistics. We show that they provide a family of locally asymptotically optimal goodness-of-fit tests, in the sense of Bahadur, for the location problem associated with (type iv) generalized logistic distributions. Our paper extends and unifies some results already known for the classical Cramér–von Mises and Anderson–Darling statistics which are optimal with respect to the hyperbolic secant and the logistic distributions.

Suggested Citation

  • Pycke, Jean-Renaud, 2021. "A new family of omega-square-type statistics with Bahadur local optimality for the location family of generalized logistic distributions," Statistics & Probability Letters, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:stapro:v:170:y:2021:i:c:s0167715220303023
    DOI: 10.1016/j.spl.2020.108999
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    References listed on IDEAS

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    1. P. Groeneboom & J. Oosterhoff, 1977. "Bahadur efficiency and probabilities of large deviations," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 31(1), pages 1-24, March.
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