caa a22 4500 475793307 CHVBK 20180406123716.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1007/s001840000059 doi (NATIONALLICENCE)springer-10.1007/s001840000059 Strong uniform convergence for the estimator of the regression function under ϕ-mixing conditions [Elektronische Daten] [Weimin Qian, Volker Mammitzsch] Abstract.: Suppose the observations (X i,Y i), i=1, , n, are ϕ-mixing. The strong uniform convergence and convergence rate for the estimator of the regression function was studied by serveral authors, e.g. G. Collomb (1984), L. Györfi et al. (1989). But the optimal convergence rates are not reached unless the Y i are bounded or the E exp (a|Y i|) are bounded for some a>0. Compared with the i.i.d. case the convergence of the Nadaraya-Watson estimator under ϕ-mixing variables needs strong moment conditions. In this paper we study the strong uniform convergence and convergence rate for the improved kernel estimator of the regression function which has been suggested by Cheng P. (1983). Compared with Theorem A in Y. P. Mack and B. Silverman (1982) or Theorem 3.3.1 in L. Györfi et al. (1989), we prove the convergence for this kind of estimators under weaker moment conditions. The optimal convergence rate for the improved kernel estimator is attained under almost the same conditions of Theorem 3.3.2 in L. Györfi et al. (1989). Springer-Verlag Berlin Heidelberg, 2000 Key words: Strong uniform convergence, convergence rate, improved kernel estimator, ϕ-mixing, nonparametric regression nationallicence Qian Weimin Department of Applied Mathematics, Tongji University, Shanghai 200092, P.R. China (e-mail: qianweimin@hotmail.com), CN aut Mammitzsch Volker Department of Mathematics and Computer Science, University of Marburg, 35032 Marburg, Germany (e-mail: mammit@mathematik.uni-marburg.de), DE aut https://doi.org/10.1007/s001840000059 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s001840000059 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Qian Weimin Department of Applied Mathematics, Tongji University, Shanghai 200092, P.R. China (e-mail: qianweimin@hotmail.com), CN aut NATIONALLICENCE 700 1- Mammitzsch Volker Department of Mathematics and Computer Science, University of Marburg, 35032 Marburg, Germany (e-mail: mammit@mathematik.uni-marburg.de), DE aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 378633767 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer