Central limit theorem for bifurcating markov chains under L2-ergodic conditions

Autor: S. Valère Bitseki Penda, Jean-François Delmas

Publikováno v: Advances in Applied Probability. 54:999-1031

Bifurcating Markov chains (BMCs) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for additive functionals of BMCs unde

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b64f08bbdbf09b7d9098842de9c86104
https://doi.org/10.1017/apr.2022.3

Local bandwidth selection for kernel density estimation in a bifurcating Markov chain model

Autor: Angelina Roche, S. Valère Bitseki Penda

Publikováno v: Journal of Nonparametric Statistics
Journal of Nonparametric Statistics, American Statistical Association, 2020, 32 (3), pp.535-562. ⟨10.1080/10485252.2020.1789125⟩

International audience; We propose an adaptive estimator for the stationary distribution of a bifurcating Markov Chain onRd. Bifurcating Markov chains (BMC for short) are a class of stochastic processes indexed by regular binary trees. A kernel estim

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7de44396763a47628693bd9c31bebb4f
https://hal.archives-ouvertes.fr/hal-03031788

Principe de déviations modérées pour des modèles bifurquants autorégressifs non-linéaires

Autor: Adélaïde Olivier, S. Valère Bitseki Penda

Publikováno v: Statistics and Probability Letters
Statistics and Probability Letters, Elsevier, 2018, 138, pp.20-26. 〈10.1016/j.spl.2018.02.037〉
Statistics and Probability Letters, Elsevier, 2018, 138, pp.20-26. ⟨10.1016/j.spl.2018.02.037⟩

International audience; Recently, nonparametric techniques have been proposed to study bifurcating autoregressive processes. One can build Nadaraya–Watson type estimators of the two autoregressive functions as in Bitseki Penda et al. (Bitseki Penda

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ba63ba3ae95fbbd6cd8be81a61a9d9c7
https://hal.archives-ouvertes.fr/hal-01710079

Transportation and concentration inequalities for bifurcating Markov chains

Autor: Mikael Escobar-Bach, Arnaud Guillin, S. Valère Bitseki Penda

Publikováno v: Bernoulli
Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2017, 23 (4B), pp.3213-3242. ⟨10.3150/16-BEJ843⟩
Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2017, 23 (4B), pp.3213-3242. 〈10.3150/16-BEJ843〉
Penda, S V B, Escobar-Bach, M & Guillin, A 2017, ' Transportation and concentration inequalities for bifurcating Markov chains ', Bernoulli, vol. 23, no. 4B, pp. 3213-3242 . https://doi.org/10.3150/16-BEJ843
Bernoulli 23, no. 4B (2017), 3213-3242

International audience; We investigate the transportation inequality for bifurcating Markov chains which are a class of processes indexed by a regular binary tree. Fitting well models like cell growth when each individual gives birth to exactly two o

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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01582161

Deviation inequalities and moderate deviations for estimators of parameters in bifurcating autoregressive models

Autor: Hacène Djellout, S. Valère Bitseki Penda

Publikováno v: Ann. Inst. H. Poincaré Probab. Statist. 50, no. 3 (2014), 806-844

The purpose of this paper is to investigate the deviation inequalities and the moderate deviation principle of the least squares estimators of the unknown parameters of general $p$th-order asymmetric bifurcating autoregressive processes, under suitab

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9f7f506679dbff6327dc9f1643c53944
https://doi.org/10.1214/13-aihp545