The chi-square error of Barron estimator of regular density is asymptotically normal

0410339 20240103182207.120060210235959.9 The chi-square error of Barron estimator of regular density is asymptotically normal 18 s. Publications of the Institute of Statistics of the University of Paris4293-110 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 12B Copernicus 579 Commission EC XE AV0Z1075907 An asymptotically normal limit law is derived for X2-divergences between a true probability density and its Barron estimates. This result is established for densities on real line satisfying certain regularity conditions, and for the estimates defined by means of partitions with numbers of cells increasing slowly, but not too slowly. BB SI http://hdl.handle.net/11104/0130429 UTIA-B 20000055 1998 Publications of the Institute of Statistics of the University of Paris Roč. 42 2/3 1998 93 110