Loi Asymptotique des Erreurs Quadratiques Intégrées des Estimateurs à Noyau de la Densité et de la Régression sous des Conditions de Dépendance

Carlos Tenreiro

Abstract: Central limit theorems for integrated squared errors of nonparametric kernel estimators of density and regression functions are established under asymptotic independence conditions as an application of central limit theorems for degenerated U-statistics. The relative stability in probability for these integrated squared errors is also established. These results generalize the corresponding ones obtained by Hall in 1984 in the independence context.

Keywords: Kernel estimator; integrated squared error; central limit theorem; U-statistic; mixing.

Classification (MSC2000): 62G20, 62G07

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