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

Peter Hall

Journal of Multivariate Analysis, 1984, vol. 14, issue 1, 1-16

Abstract: 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.

Keywords: central; limit; theorem; integrated; square; error; Martingale; nonparametric; density; estimator; U-statistic (search for similar items in EconPapers)
Date: 1984
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Citations: View citations in EconPapers (166)

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