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New Multivariate Product Density Estimators by Luc Devroye; Adam Krzyżak is a scholarly article available to read on EtoBox.

What is New Multivariate Product Density Estimators about?

Let X be an R d -valued random variable with unknown density f. Let X 1 , ..., X n be i.i.d. random variables drawn from f. The objective is to estimate f(x), where x=(x 1 , ..., x d ). We study the pointwise convergence of two new density estimates, the Hilbert product kernel estimate where X i =(X i1 , ..., X id ), and the Hilbert k-nearest neighbor estimate where ), and X (k) is the kth nearest neighbor of x when points are ordered by increasing values of the product < d j=1 |x j -X (k) j |, and k=o(log n), k Q .. The auxiliary results needed permit us to formulate universal consistency results (pointwise and in L 1 ) for product kernel estimates with different window widths for each coordinate, and for rectangular partitioning and tree estimates. In particular, we show that locally adapted smoothing factors for product kernel estimates may make the kernel estimate inconsistent even under standard conditions on the bandwidths.

Author

Luc Devroye; Adam Krzyżak

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0047-259X)

Published

2002

Language

EN