Displaying similar documents to “Model selection for (auto-)regression with dependent data”

Model selection for regression on a random design

Yannick Baraud (2002)

ESAIM: Probability and Statistics

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We consider the problem of estimating an unknown regression function when the design is random with values in ℝ k . Our estimation procedure is based on model selection and does not rely on any prior information on the target function. We start with a collection of linear functional spaces and build, on a data selected space among this collection, the least-squares estimator. We study the performance of an estimator which is obtained by modifying this least-squares estimator on a set of...

Sensitivity analysis of M -estimators of non-linear regression models

Asunción Rubio, Francisco Quintana, Jan Ámos Víšek (1994)

Commentationes Mathematicae Universitatis Carolinae

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An asymptotic formula for the difference of the M -estimates of the regression coefficients of the non-linear model for all n observations and for n - 1 observations is presented under conditions covering the twice absolutely continuous ϱ -functions. Then the implications for the M -estimation of the regression model are discussed.

Histogram selection in non Gaussian regression

Marie Sauvé (2009)

ESAIM: Probability and Statistics

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We deal with the problem of choosing a piecewise constant estimator of a regression function mapping 𝒳 into ℝ . We consider a non Gaussian regression framework with deterministic design points, and we adopt the non asymptotic approach of model selection penalization developed by Birgé and Massart. Given a collection of partitions of 𝒳 , with possibly exponential complexity, and the corresponding collection of piecewise constant estimators, we propose a penalized least squares criterion...

A note on the rate of convergence of local polynomial estimators in regression models

Friedrich Liese, Ingo Steinke (2001)

Kybernetika

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Local polynomials are used to construct estimators for the value m ( x 0 ) of the regression function m and the values of the derivatives D γ m ( x 0 ) in a general class of nonparametric regression models. The covariables are allowed to be random or non-random. Only asymptotic conditions on the average distribution of the covariables are used as smoothness of the experimental design. This smoothness condition is discussed in detail. The optimal stochastic rate of convergence of the estimators is established....