Uniform consistency of automatic and location-adaptive delta-sequence estimators |
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Authors: | Deborah Nolan J Stephen Marron |
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Institution: | (1) Department of Statistics, University of California, 94720 Berkeley, CA;(2) Department of Statistics, University of North Carolina, 27514 Chapel Hill, NC |
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Abstract: | Summary The class of delta-sequence estimators for a probability density includes the kernel, histogram and orthogonal series types, because each can be characterized as a collection of averages of some function that is indexed by a smoothing parameter. There are two important extensions of this class. The first allows a random smoothing parameter, for example that specified by a cross-validation method. The second allows the smoothing parameter to be a function of location, for example an estimator based on nearest-neighbor distance. In this paper a general method is presented which establishes uniform consistency for all of these estimators.Research partially supported by AFOSR Grant No. S-49620-82-C-0144, and by NSF Grant DMS-850-3347Research supported by NSF Grant DMS-8400602 |
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