On a multidimensional general bootstrap for empirical estimator of continuous-time semi-Markov kernels with applications

Bouzebda, Salim; Papamichail, Chrysanthi; Limnios, Nikolaos

doi:10.1080/10485252.2017.1404059

Cited by 10 publications

(4 citation statements)

References 51 publications

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“…To circumvent this, in the present paper, we have established the analogous results of Bae, J., Jun, D., and Levental, S. [2] for the bootstrap martingale-difference array random processes in an extended framework. Our results can be applied in the semi-Markov setting to construct confidence bands as Bouzebda, S., Papamichail, Ch., and Limnios, N. [10]. We mention also that the present paper largely extends the scope of applications of the last mentioned paper.…”

Section: Discussionsupporting

confidence: 64%

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Exchangeably Weighted Bootstraps of Martingale Difference Arrays under the Uniformly Integrable Entropy

Bouzebda

Limnios

2020

josa

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Section: Discussionsupporting

confidence: 64%

“…Comments. Let us recall some comments from Bouzebda, S., Papamichail, Ch., and Limnios, N. [10]. Barbe, P. and Bertail, P. [3] discussed in details some properties of the weighted bootstrap for general von Mises functionals.…”

Section: Resultsmentioning

confidence: 99%

Exchangeably Weighted Bootstraps of Martingale Difference Arrays under the Uniformly Integrable Entropy

Bouzebda

Limnios

2020

josa

Self Cite

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“…P is an independent copy of the Gaussian process G P defined in Theorem 3.3. Application of Theorem 4.2, is well documented, we may refer for example to [11,13,14,17,26,27,33,35,132,133]. Remark 4.3.…”

Section: Theorem 41 Suppose That the Copula Density C(• •) Is Continu...mentioning

confidence: 99%

On the weak convergence and the uniform-in-bandwidth consistency of the general conditional $U$-processes based on the copula representation: multivariate setting

BOUZEBDA

2023

Hacettepe Journal of Mathematics and Statistics

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U-statistics represent a fundamental class of statistics from modeling quantities of interest defined by multi-subject responses. U-statistics generalise the empirical mean of a random variable X to sums over every m-tuple of distinct observations of X. Stute [Conditional U -statistics, Ann. Probab., 1991] introduced a class of estimators called conditional U-statistics. In the present work, we provide a new class of estimators of conditional U-statistics. More precisely, we investigate the conditional U-statistics based on copula representation. We establish the uniform-in-bandwidth consistency for the proposed estimator. In addition, uniform consistency is also established over φ ∈ Ƒ for a suitably restricted class Ƒ, in both cases bounded and unbounded, satisfying some moment conditions. Our theorems allow data-driven local bandwidths for these statistics. Moreover, in the same context, we show the uniform bandwidth consistency for the nonparametric Inverse Probability of Censoring Weighted estimators of the regression function under random censorship, which is of its own interest. We also consider the weak convergence of the conditional U-statistics processes. We discuss the wild bootstrap of the conditional U-statistics processes. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis class of functions and some mild conditions on the model.

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“…These different weights lead to a general approach to study the class of exchangeable bootstrap weights, originally studied by Mason and Newton (1992) and subsequently by Praestgaard and Wellner (1993), Janssen and Pauls (2003), and Janssen ( 2005) among others. An interesting application of exchangeable weighted bootstrap appears in the work of Bouzebda et al (2017).…”

Section: The Proposed Weighted Bootstrapmentioning

confidence: 99%

On the performance of weighted bootstrapped kernel deconvolution density estimators

2018

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Where a licence is displayed above, please note the terms and conditions of the licence govern your use of this document.When citing, please reference the published version. Take down policyWhile the University of Birmingham exercises care and attention in making items available there are rare occasions when an item has been uploaded in error or has been deemed to be commercially or otherwise sensitive.

show abstract

On a multidimensional general bootstrap for empirical estimator of continuous-time semi-Markov kernels with applications

Cited by 10 publications

References 51 publications

Exchangeably Weighted Bootstraps of Martingale Difference Arrays under the Uniformly Integrable Entropy

Exchangeably Weighted Bootstraps of Martingale Difference Arrays under the Uniformly Integrable Entropy

On the weak convergence and the uniform-in-bandwidth consistency of the general conditional $U$-processes based on the copula representation: multivariate setting

On the performance of weighted bootstrapped kernel deconvolution density estimators

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