Local efficiency of integrated goodness-of-fit tests under skew alternatives

Durio, Alessandra; Nikitin, Ya. Yu.

doi:10.1016/j.spl.2016.05.016

Cited by 4 publications

(1 citation statement)

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“…The asymptotic behavior of weighted multivariate Cramér-von Mises-type statistics under contiguous alternatives was characterized by Bouzebda and Zari (2013). For more recent references, we refer to Durio and Nikitin (2016), Bouzebda (2016) and Alvarez-Andrade et al (2017). The main purpose of this paper is to investigate the strong approximation of the p-fold integrated empirical process.…”

Section: Introductionmentioning

confidence: 99%

Strong approximations for the p-fold integrated empirical process with applications to statistical tests

Alvarez-Andrade

Bouzebda

Lachal

2017

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The main purpose of this paper is to investigate the strong approximation of the p-fold integrated empirical process, p being a fixed positive integer. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer process. Our arguments are based in part on the Komlós et al. (1975)'s results. We obtain an exponential bound for the tail probability of the weighted approximation to the p-fold integrated empirical process. Applications include the two-sample testing procedures together with the change-point problems. We also consider the strong approximation of integrated empirical processes when the parameters are estimated. We study the behavior of the self-intersection local time of the partial sum process representation of integrated empirical processes. Finally, simulation results are provided to illustrate the finite sample performance of the proposed statistical tests based on the integrated empirical processes.

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