Title: Optimization of Barron density estimates
Authors: Vajda, I ×
van der Meulen, Edward #
Issue Date: Jul-2001
Publisher: Institute of Electrical and Electronics Engineers
Series Title: IEEE Transactions on Information Theory vol:47 issue:5 pages:1867-1883
Abstract: We investigate a nonparametric estimator of probability density introduced by A. R, Barren. Earlier papers established its consistency in a strong sense, e.g,, in the expected information divergence or expected chi-square divergence. This paper pays main attention to the expected chi-square divergence criterion. We give a new motivation of the Barren estimator by showing that a maximum-likelihood estimator (MLE) of a density from a family important in practice is consistent in expected information divergence but not in expected chi-square divergence. We also present new and practically applicable conditions of consistency in the expected chi-square divergence. Main attention is paid to optimization tin the sense of the mentioned criterion) of the two objects specifying the Barren estimator: the dominating probability density and the decomposition of the observation space into finitely many bins. Both problems are explicitly solved under certain regularity assumptions about the estimated density. A simulation study illustrates the results in exponential, Rayleigh, and Weibull families.
ISSN: 0018-9448
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Statistics Section
Mathematics - miscellaneous
× corresponding author
# (joint) last author

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