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| HAL: hal-00563638, version 1 |
| DOI: 10.3150/10-BEJ347 |
| Detailed view |  Export this paper |
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| Bernoulli 18, 2 (2012) 703-734 |
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| A uniform Berry-Esseen theorem on M-estimators for geometrically ergodic Markov chains |
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| Loïc Hervé 1James Ledoux 1 |
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| (2012) |
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| Let $\{X_{n}\}_{n\geq 0}$ be a $V$-geometrically ergodic Markov chain. Given some real-valued functional $F$, define $M_{n}(\alpha):=n^{-1}\sum^{n}_{k=1} F(\alpha, X_{k-1}, X_{k}), \alpha \in \mathcal A \subset \mathbb R$. Consider an $M$-estimator $\widehat{\alpha}_{n}$, that is as a measurable function of the observations satisfying $M_{n} (v)\leq min_{\alpha \in\mathcal A} M_{n}(\alpha)+ c_{n}$ with $\{c_{n}\}_{n\leq 1}$ some sequence of real numbers going to zero. Under some standard regularity and moment assumptions, close to those of the i.i.d. case, the estimator $\widehat{\alpha}_{n}$ satisfies a Berry-Esseen theorem uniformly with respect to the underlying probability distribution of the Markov chain. |
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| 1: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 2: | Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI) |
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Ensai, Ecole Nationale de la Statistique et de l'Analyse de l'Information |
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| Théorie ergodique Statistique |
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| Subject | : | Mathematics/Statistics Statistics/Statistics Theory Mathematics/Probability |
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| Spectral method |
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| hal-00563638, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00563638 | |
| oai:hal.archives-ouvertes.fr:hal-00563638 | |
| From: Marie-Annick Guillemer | |
| Submitted on: Monday, 7 February 2011 09:44:06 | |
| Updated on: Monday, 10 September 2012 10:17:49 | |
