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Yunshyong Chow, S. Geman, L.-D. Wu (1983)
Consistent Cross-Validated Density EstimationAnnals of Statistics, 11
A. Dvoretzky, J. Kiefer, J. Wolfowitz (1956)
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In this paper we investigate the problem of estimating thed-dimensional probability densityf(x),x∈R d from a sample of sizen. The non-parametric estimator is the data based histogramf n (x) as defined in (1). Under suitable conditions, we have proved theL 1-norm consistance of this estimate, that is $$\mathop {\lim }\limits_{n \to \infty } \int_{R^a } {|f(x) - f_n (x)|dx = 0,{\text{ a}}{\text{.s}}{\text{.}}}$$
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Apr 25, 2005
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