A new approach to goodness-of-fit testing based on the integrated empirical process<sup>*</sup>

Henze, Norbert; Nikitin, Yakov

doi:10.1080/10485250008832815

Cited by 33 publications

(53 citation statements)

References 16 publications

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“…Henze and Nikitin (2003) considered a two-sample testing procedure and focused on the approximate local Bahadur efficiencies of their statistical tests. It is noteworthy to point out that tests based on some integrated empirical processes turn out to be more efficient for certain distributions, we may refer at this point to Henze and Nikitin (2003, 2002. In Henze and Nikitin (2003), it is shown that the statistics based on the integrated empirical processes perform better the classical ones, under asymmetric alternatives.…”

Section: Introductionmentioning

confidence: 99%

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

Alvarez-Andrade

Bouzebda

Lachal

2017

TEST

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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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Section: Introductionmentioning

confidence: 99%

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

Alvarez-Andrade

Bouzebda

Lachal

2017

TEST

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“…For the completeness of the paper, we provide here a proof of (1.6) inspired by Henze and Nikitin (2002). The function F n can be computed as follows: for any n ∈ N * and any t ∈ R,…”

Section: Proof Of Formula (16)mentioning

confidence: 99%

“…This characterization is possible by making use of a representation provided by Henze and Nikitin (2002) that expresses the integrated empirical process in terms of a partial sums process, see (6.1) below. Recall the definition of the process given in (1.4).…”

Section: Local Time Of the Integrated Empirical Processmentioning

confidence: 99%

“…A n = β n (1). According to Henze and Nikitin (2002) p. 185, we have the following representation for A n :…”

Section: Local Time Of the Integrated Empirical Processmentioning

confidence: 99%

“…From Theorem II.1 of Henze and Nikitin (2002) (see also the self-contained proof given in Section 7), we learn that, almost surely, F n (t) = 1 2 F n (t) 2 + 1 n F n (t) for t ∈ R, n ∈ N * .…”

Section: Introductionmentioning

confidence: 99%

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Some asymptotic results for the integrated empirical process with applications to statistical tests

Alvarez-Andrade

Bouzebda

Lachal

2016

Communications in Statistics - Theory and Methods

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The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. 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. Applications include the two-sample testing procedures together with the change-point problems. We also consider the strong approximation of the integrated empirical process when the parameters are estimated. Finally, we study the behavior of the self-intersection local time of the partial sum process representation of the integrated empirical process.

show abstract

Statistical inference for $$L^2$$ L 2 -distances to uniformity

2018

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A new approach to goodness-of-fit testing based on the integrated empirical process^*

Cited by 33 publications

References 16 publications

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

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

Some asymptotic results for the integrated empirical process with applications to statistical tests

Statistical inference for $$L^2$$ L 2 -distances to uniformity

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A new approach to goodness-of-fit testing based on the integrated empirical process*

Cited by 33 publications

References 16 publications

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

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

Some asymptotic results for the integrated empirical process with applications to statistical tests

Statistical inference for $$L^2$$ L 2 -distances to uniformity

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Product

Resources

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A new approach to goodness-of-fit testing based on the integrated empirical process^*