Asymptotic law of the intergrated quadratic errors of kernel density and regression estimators under the conditions of dependence. (Loi asymptotique des erreurs quadratiques intégrées des estimateurs à noyau de la densité et de la régression sous des conditions de dépendance.) (French) Zbl 0873.62042

Tenreiro, Carlos

Port. Math. 54, No. 2, 187-213 (1997).

Summary: 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 P. Hall [Ann. Stat. 12, 241-260 (1984; Zbl 0544.62036)] in the independence context.

MSC:

62G07	Density estimation
62G20	Asymptotic properties of nonparametric inference

Keywords:

integrated squared errors; asymptotic independence conditions; central limit theorems; degenerated \(U\)-statistics