Eric Matzner-Løber

Bandwidth selection for local linear regression smoothers

Summary. The paper presents a general strategy for selecting the bandwidth of nonparametric regression estimators and specializes it to local linear regression smoothers. The procedure requires the sample to be divided into a training sample and a testing sample. Using the training sample we first compute a family of regression smoothers indexed by their bandwidths. Next we select the bandwidth by minimizing the empirical quadratic prediction error on the testing sample. The resulting bandwidth satisfies a finite sample oracle inequality which holds for all bounded regression functions. This permits asymptotically optimal estimation for nearly any regression function. The practical performance of the method is illustrated by a simulation study which shows good finite sample behaviour of our method compared with other bandwidth selection procedures.

Inférence dans le modèle gaussien

Nous rappelons le contexte du chapitre precedent :

La régression linéaire simple

{Y_{n \times 1}} = {X_{n \times p}} {\beta _{p \times 1}} + {\varepsilon _{n \times 1}},

La régression linéaire multiple

, sous les hypotheses H1 : rang(X) = p. \({\mathcal{H}_2}:\mathbb{E}\left( \varepsilon \right) = 0, {\Sigma _\varepsilon } = {\sigma ^2} {I_n}.\)

Régression sur variables qualitatives

Nous rappelons le contexte :

Choix de variables

{Y_{n \times 1}} = {X_{n \times p}} {\beta _{p \times 1}} + {\varepsilon _{n \times 1}},