ISSN:
1435-926X
Keywords:
Key words: Strong uniform convergence, convergence rate, improved kernel estimator, ϕ-mixing, nonparametric regression.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s001840000059
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