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Argmax-stable marked empirical processes

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  • Ferger, Dietmar

Abstract

We consider a marked empirical process corresponding to a sample X1,...,Xn of independent and identically distributed random variables and exchangeable random marks C1,...,Cn. If the sum of all marks is equal to zero, then there exists a certain order statistic with random index, which is a maximizing point of the process. It is shown that for each finite sample size this point of maximum has the same distribution as X1 (argmax-stability). As an application we derive the exact distribution of an estimator for the discontinuity point in a regression function.

Suggested Citation

  • Ferger, Dietmar, 2009. "Argmax-stable marked empirical processes," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1203-1206, May.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:9:p:1203-1206
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    References listed on IDEAS

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    1. Winfried Stute & Li‐Xing Zhu, 2002. "Model Checks for Generalized Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 535-545, September.
    2. Escanciano, J. Carlos, 2007. "Weak convergence of non-stationary multivariate marked processes with applications to martingale testing," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1321-1336, August.
    3. Astrid Dempfle & Winfried Stute, 2002. "Nonparametric estimation of a discontinuity in regression," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(2), pages 233-242, May.
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    Cited by:

    1. Habibi Reza, 2011. "Exact Distribution of Argmax (Argmin)," Stochastics and Quality Control, De Gruyter, vol. 26(2), pages 155-162, January.

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