"Barron estimator; chi-square criterion; density estimation"@en . "47" . "We investigate a nonparametric estimator of probability density introduced by A.R.Barron. 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 Barron estimators by showing that a maximum-likelihood estimator (MLE) of a density from a family important in practice is consistent in expected information divergence." . "van der Meulen, E. C." . . . "690318" . . . . . . "Optimization of Barron density estimates."@en . "Optimization of Barron density estimates." . "0018-9448" . "Optimization of Barron density estimates."@en . . . "1867;1883" . . . "[CDE3BD2B6474]" . "Optimization of Barron density estimates." . "P(GA102/99/1137), Z(AV0Z1075907)" . "We investigate a nonparametric estimator of probability density introduced by A.R.Barron. 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 Barron estimators by showing that a maximum-likelihood estimator (MLE) of a density from a family important in practice is consistent in expected information divergence."@en . "Vajda, Igor" . "RIV/67985556:_____/01:16010060!RIV/2003/AV0/A16003/N" . . "RIV/67985556:_____/01:16010060" . . "5" . . . "1"^^ . . "17"^^ . . "0"^^ . "0"^^ . "2"^^ . "IEEE Transactions on Information Theory" . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" .