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Central limit theorem for integrated square error of multivariate nonparametric density estimators

1984; Elsevier BV; Volume: 14; Issue: 1 Linguagem: Inglês

10.1016/0047-259x(84)90044-7

1095-7243

Peter Hall,

Bayesian Methods and Mixture Models

Martingale theory is used to obtain a central limit theorem for degenerate U-statistics with variable kernels, which is applied to derive central limit theorems for the integrated square error of multivariate nonparametric density estimators. Previous approaches to this problem have employed Komlós-Major-Tusnády type approximations to the empiric distribution function, and have required the following two restrictive assumptions which are not necessary using the present approach: (i) the data are in one or two dimensions, and (ii) the estimator is constructed suboptimally.