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Topics in global convergence of density estimatesThe problem of estimating a density f on R sup d from a sample Xz(1),...,X(n) of independent identically distributed random vectors is critically examined, and some recent results in the field are reviewed. The following statements are qualified: (1) For any sequence of density estimates f(n), any arbitrary slow rate of convergence to 0 is possible for E(integral/f(n)-fl); (2) In theoretical comparisons of density estimates, integral/f(n)-f/ should be used and not integral/f(n)-f/sup p, p 1; and (3) For most reasonable nonparametric density estimates, either there is convergence of integral/f(n)-f/ (and then the convergence is in the strongest possible sense for all f), or there is no convergence (even in the weakest possible sense for a single f). There is no intermediate situation.
Document ID
19830007504
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Devroye, L.
(McGill Univ. Montreal Quebec, Canada)
Date Acquired
August 11, 2013
Publication Date
January 1, 1982
Publication Information
Publication: Texas A and M Univ. Proc. of the NASA Workshop on Density Estimation and Function Smoothing
Subject Category
Earth Resources And Remote Sensing
Accession Number
83N15775
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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