This paper considers the convergence rates for nonparametric estimators of the error distribution in semi-parametric regression models. By establishing some general laws of the iterated logarithm, it shows that the ra...This paper considers the convergence rates for nonparametric estimators of the error distribution in semi-parametric regression models. By establishing some general laws of the iterated logarithm, it shows that the rates of convergence of either the empirical distribution or a smoothed version of the empirical distribution function matches exactly the rates obtained for an independent sample from the error distribution.展开更多
In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for ...In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes.展开更多
Given a sequence of mixing random variables {X1,Xn;n≥1} taking values in a separable Banach space B,and Sn denoting the partial sum,a general law of the iterated logarithm is established,that is,we have with probabil...Given a sequence of mixing random variables {X1,Xn;n≥1} taking values in a separable Banach space B,and Sn denoting the partial sum,a general law of the iterated logarithm is established,that is,we have with probability one,lim supn→∞‖Sn‖/cn = α0 < ∞ for a regular normalizing sequence {cn}1,where α 0 is a precise value.展开更多
基金supported by the National Science Foundation of China under Grant Nos.11201422,11301481,and 11371321Zhejiang Provincial Natural Science Foundation of China under Grant Nos.Y6110639,Y6110110,LQ12A01018,and LQ12A01017+2 种基金the National Statistical Science Research Project of China under Grant No.2012LY174Foundation for Young Talents of ZJGSU under Grant No.1020XJ1314019Zhejiang Provincial Key Research Base for Humanities and Social Science Research(Statistics)
文摘This paper considers the convergence rates for nonparametric estimators of the error distribution in semi-parametric regression models. By establishing some general laws of the iterated logarithm, it shows that the rates of convergence of either the empirical distribution or a smoothed version of the empirical distribution function matches exactly the rates obtained for an independent sample from the error distribution.
基金the National Natural Science Foundation of China (Grant Nos.10671176,10771192)
文摘In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes.
基金supported by National Natural Science Foundation of China (Grant Nos. 10901138,11071213,11026087)supported by National Natural Science Foundation of China (Grant No.11071214)+1 种基金Natural Science Foundation of Zhejiang Province (Grant No.R6100119)Program for New Century Excellent Talents in University
文摘Given a sequence of mixing random variables {X1,Xn;n≥1} taking values in a separable Banach space B,and Sn denoting the partial sum,a general law of the iterated logarithm is established,that is,we have with probability one,lim supn→∞‖Sn‖/cn = α0 < ∞ for a regular normalizing sequence {cn}1,where α 0 is a precise value.
