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Limit theorems for rank statistics

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  • Husková, M.

Abstract

The purpose of the paper is to extend the weak asymptotic results for the weighted partial sums of i.i.d. random variables to the weighted partial sums of rank scores. These results then suggest various test procedures for the change point problem. The crucial tools in the proofs are martingale property of a class of two-sample rank statistics and the Hájek results (1961) of the simple linear rank statistics.

Suggested Citation

  • Husková, M., 1997. "Limit theorems for rank statistics," Statistics & Probability Letters, Elsevier, vol. 32(1), pages 45-55, February.
    • Handle: RePEc:eee:stapro:v:32:y:1997:i:1:p:45-55
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    References listed on IDEAS

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    1. Yao, Yi-Ching, 1990. "On the asymptotic behavior of a class of nonparametric tests for a change-point problem," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 173-177, February.
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    Cited by:

    1. Oka, Tatsushi & Qu, Zhongjun, 2011. "Estimating structural changes in regression quantiles," Journal of Econometrics, Elsevier, vol. 162(2), pages 248-267, June.
    2. Horváth, Lajos & Shao, Qi-Man, 2007. "Limit theorems for permutations of empirical processes with applications to change point analysis," Stochastic Processes and their Applications, Elsevier, vol. 117(12), pages 1870-1888, December.
    3. Antoch, Jaromír & Husková, Marie, 2001. "Permutation tests in change point analysis," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 37-46, May.
    4. Husková, M., 2003. "Serial rank statistics for detection of changes," Statistics & Probability Letters, Elsevier, vol. 61(2), pages 199-213, January.

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