Displaying similar documents to “Adaptive estimation of the transition density of a Markov chain”

Adaptive estimation of the conditional intensity of marker-dependent counting processes

F. Comte, S. Gaïffas, A. Guilloux (2011)

Annales de l'I.H.P. Probabilités et statistiques

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We propose in this work an original estimator of the conditional intensity of a marker-dependent counting process, that is, a counting process with covariates. We use model selection methods and provide a nonasymptotic bound for the risk of our estimator on a compact set. We show that our estimator reaches automatically a convergence rate over a functional class with a given (unknown) anisotropic regularity. Then, we prove a lower bound which establishes that this rate is optimal. Lastly,...

Change-point estimation from indirect observations. 1. Minimax complexity

A. Goldenshluger, A. Juditsky, A. B. Tsybakov, A. Zeevi (2008)

Annales de l'I.H.P. Probabilités et statistiques

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We consider the problem of nonparametric estimation of signal singularities from indirect and noisy observations. Here by singularity, we mean a discontinuity (change-point) of the signal or of its derivative. The model of indirect observations we consider is that of a linear transform of the signal, observed in white noise. The estimation problem is analyzed in a minimax framework. We provide lower bounds for minimax risks and propose rate-optimal estimation procedures.

The integrated squared error estimation of parameters.

Jamal-Dine Chergui (1996)

Extracta Mathematicae

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This paper deals with the problem of estimation in the parametric case for discrete random variables. Their study is facilitated by the powerful method of probability generating function.