Mean Square Error for Histograms when Estimating Radon-Nikodym Derivatives

Paulo Eduardo Oliveira

Abstract: The use of histograms for estimation of Radon-Nikodym derivatives is addressed. Some results concerning the convergence have been established with no reference about the behaviour of the error. In this paper we study the mean square convergence rate of this error. The optimization of the partitions on which the histograms are based thus obtained recovers the $n^{-2/(p+2)}$ rate known for some problems that are included in this more general framework.

Keywords: Point process; histogram; convergence rate.

Classification (MSC2000): 62G05, 62G20.

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