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Asymptotic properties of goodness of fit tests based on higher order overlapping spacings

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  • Mirakhmedov, Sherzod M.

Abstract

The paper is devoted to tests for uniformity based on sum-functions of overlapping spacings, where the order of spacings can diverge to infinity as the sample size increases. In particular, it is shown that the asymptotic local power and Pitman asymptotic relative efficiencies of these tests depend significantly on the asymptotic properties of the counterpart statistics based on disjoint spacings. The general results are applied to a family of tests based on power divergence statistics.

Suggested Citation

  • Mirakhmedov, Sherzod M., 2025. "Asymptotic properties of goodness of fit tests based on higher order overlapping spacings," Statistics & Probability Letters, Elsevier, vol. 225(C).
    • Handle: RePEc:eee:stapro:v:225:y:2025:i:c:s0167715225001063
    DOI: 10.1016/j.spl.2025.110461
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    References listed on IDEAS

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    1. S. Jammalamadaka & Xian Zhou & Ram Tiwari, 1989. "Asymptotic efficiencies of spacings tests for goodness of fit," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 355-377, December.
    2. Sherzod M. Mirakhmedov & S. Rao Jammalamadaka, 2013. "Higher-order expansions and efficiencies of tests based on spacings," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 339-359, June.
    3. Hall, Peter, 1986. "On powerful distributional tests based on sample spacings," Journal of Multivariate Analysis, Elsevier, vol. 19(2), pages 201-224, August.
    4. Xian Zhou & S. Jammalamadaka, 1989. "Bahadur efficiencies of spacings tests for goodness of fit," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(3), pages 541-553, September.
    5. Sherzod Mirakhmedov & Syed Tirmizi & Muhammad Naeem, 2011. "A Cramér-type large deviation theorem for sums of functions of higher order non-overlapping spacings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(1), pages 33-54, July.
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