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Article Dans Une Revue Mathematical Methods of Statistics Année : 2009

Estimation of the density of regression errors by pointwise model selection

Résumé

This paper presents two results: a density estimator and an estimator of regression error density. We first propose a density estimator constructed by model selection, which is adaptive for the quadratic risk at a given point. Then we apply this result to estimate the error density in a homoscedastic regression framework Y i = b(X i ) + ε i from which we observe a sample (X i , Y i ). Given an adaptive estimator b^ of the regression function, we apply the density estimation procedure to the residuals ε^i=Yi−b^(Xi) . We get an estimator of the density of ε i whose rate of convergence for the quadratic pointwise risk is the maximum of two rates: the minimax rate we would get if the errors were directly observed and the minimax rate of convergence of b^ for the quadratic integrated risk.

Dates et versions

hal-02657242 , version 1 (30-05-2020)

Identifiants

Citer

Sandra Plancade. Estimation of the density of regression errors by pointwise model selection. Mathematical Methods of Statistics, 2009, 18 (4), pp.313-347. ⟨10.3103/S1066530709040036⟩. ⟨hal-02657242⟩
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