Displaying similar documents to “On adaptive estimation in nonlinear regression”

Linear versus quadratic estimators in linearized models

Lubomír Kubáček (2004)

Applications of Mathematics

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In nonlinear regression models an approximate value of an unknown parameter is frequently at our disposal. Then the linearization of the model is used and a linear estimate of the parameter can be calculated. Some criteria how to recognize whether a linearization is possible are developed. In the case that they are not satisfied, it is necessary to take into account either some quadratic corrections or to use the nonlinear least squares method. The aim of the paper is to find some criteria...

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.

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. 2. Adaptation

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

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

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We focus on the problem of adaptive estimation of signal singularities from indirect and noisy observations. A typical example of such a singularity is a discontinuity (change-point) of the signal or of its derivative. We develop a change-point estimator which adapts to the unknown smoothness of a nuisance deterministic component and to an unknown jump amplitude. We show that the proposed estimator attains optimal adaptive rates of convergence. A simulation study demonstrates reasonable...