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On powerful distributional tests based on sample spacings

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  • Hall, Peter

Abstract

This paper is devoted to tests for uniformity based on sum-functions of m-spacings, where m diverges to infinity as the sample size, n, increases. It is shown that if m diverges at a slower rate than n1/2 then the commonly used sum-function will detect alternatives distant (mn)-1/4 from the uniform. This result fails if m diverges more quickly than n1/2, and in that situation the statistic must be modified. The case where m/n --> [varrho], 0

Suggested Citation

  • Hall, Peter, 1986. "On powerful distributional tests based on sample spacings," Journal of Multivariate Analysis, Elsevier, vol. 19(2), pages 201-224, August.
    • Handle: RePEc:eee:jmvana:v:19:y:1986:i:2:p:201-224
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    Cited by:

    1. Reschenhofer, Erhard, 1997. "Generalization of the Kolmogorov-Smirnov test," Computational Statistics & Data Analysis, Elsevier, vol. 24(4), pages 433-441, June.
    2. Hino, Hideitsu & Koshijima, Kensuke & Murata, Noboru, 2015. "Non-parametric entropy estimators based on simple linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 72-84.
    3. Jan G. De Gooijer & Ao Yuan, 2008. "MDL Mean Function Selection in Semiparametric Kernel Regression Models," Tinbergen Institute Discussion Papers 08-046/4, Tinbergen Institute.
    4. Menéndez, M. & Morales, D. & Pardo, L., 1997. "Maximum entropy principle and statistical inference on condensed ordered data," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 85-93, May.
    5. Ao Yuan & Jan G. De Gooijer, 2007. "Semiparametric Regression with Kernel Error Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 841-869, December.
    6. Huffer, Fred W. & Chien-Tai Lin, 1997. "Computing the exact distribution of the extremes of sums of consecutive spacings," Computational Statistics & Data Analysis, Elsevier, vol. 26(2), pages 117-132, December.
    7. Ao Yuan, 2009. "Semiparametric inference with kernel likelihood," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(2), pages 207-228.
    8. Penrose, Mathew D., 2000. "Central limit theorems for k-nearest neighbour distances," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 295-320, February.
    9. Nelly Litvak & Maria Vlasiou, 2010. "A survey on performance analysis of warehouse carousel systems," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(4), pages 401-447, November.

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