0410591 20240103182225.020060210235959.9 17 s. cav_un_epca*02567230018-9448475 (2001)1867-1883Institute of Electrical and Electronics Engineers Barron estimator chi-square criterion density estimation cav_un_auth*0101218 Vajda Igor UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0211827 van der Meulen E. C. BE 09J 579 Copernicus XE GA102/99/1137 GA ČR cav_un_auth*0004432 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. BD SI http://hdl.handle.net/11104/0130680 UTIA-B 20010060 2001 cav_un_epca*0256723 IEEE Transactions on Information Theory 0018-9448 1557-9654 Roč. 47 č. 5 2001 1867 1883 Institute of Electrical and Electronics Engineers