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Weak convergence of weighted empirical type processes under contiguous and changepoint alternatives

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  • Szyszkowicz, Barbara

Abstract

Let X1, X2,... be independent random variables. We study asymptotic behaviour of two-time parameter empirical type processes based on observations, ranks and sequential ranks. We introduce weight functions and derive the limiting distributions of these processes under the null hypothesis of Xi being identically distributed, as well as under a class of continguous alternatives which can accommodate the possible occurrence of a changepoint in the series of measurements.

Suggested Citation

  • Szyszkowicz, Barbara, 1994. "Weak convergence of weighted empirical type processes under contiguous and changepoint alternatives," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 281-313, April.
    • Handle: RePEc:eee:spapps:v:50:y:1994:i:2:p:281-313
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    Cited by:

    1. Sergio Alvarez-Andrade & Salim Bouzebda & Aimé Lachal, 2018. "Strong approximations for the p-fold integrated empirical process with applications to statistical tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 826-849, December.
    2. Zhang, Hanqin, 2000. "On a weighted embedding for generalized pontograms," Stochastic Processes and their Applications, Elsevier, vol. 88(2), pages 213-224, August.
    3. McKeague, Ian W. & Sun, Yanqing, 1996. "Transformations of Gaussian random fields to Brownian sheet and nonparametric change-point tests," Statistics & Probability Letters, Elsevier, vol. 28(4), pages 311-319, August.

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