caa a22 4500 465811639 CHVBK 20180323112117.0 cr unu---uuuuu 170327e19900601xx s 000 0 eng 10.1007/BF02107595 doi (NATIONALLICENCE)springer-10.1007/BF02107595 Necessary and sufficient conditions for the convergence of integrated and mean-integrated r -th order error of histogram density estimates [Elektronische Daten] [Chen Xiru, Zhao Lincheng] Suppose thatX l ,..., X n are samples drawn from a population with density functionf andf n (x)=f n (x;X l ,..., X n is an estimate off(x), Denote bym nr =∫|f n (x)−f(n)| r dx andM nr =E(m nr) the Integratedr-th Order Error and Mean Integratedr-th Order Error off n for somer⩾1 (whenr=2,they are the familiar and widely studied ISE and MISE), In this paper the same necessary and sufficient condition for $$\mathop {\lim }\limits_{n \to \infty } Mnr = 0$$ and $$\mathop {\lim }\limits_{n \to \infty } m_{nr} = 0$$ a.s. is obtained whenf n (x) is the ordinary histogram estimator. Springer-Verlag, 1990 Xiru Chen Department of Mathematics, University of Science and Technology of China, China aut Lincheng Zhao Department of Mathematics, University of Science and Technology of China, China aut Acta Mathematica Sinica Springer-Verlag 6/2(1990-06-01), 178-188 1439-8516 6:2<178 1990 6 10114 https://doi.org/10.1007/BF02107595 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02107595 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Xiru Chen Department of Mathematics, University of Science and Technology of China, China aut NATIONALLICENCE 700 1- Lincheng Zhao Department of Mathematics, University of Science and Technology of China, China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica Springer-Verlag 6/2(1990-06-01), 178-188 1439-8516 6:2<178 1990 6 10114 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer