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| 1 | A LIL for independent non-identically distributed random variables in Banach space and its applications显示文摘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. | LIU WeiDong FU KeAng ZHANG LiXin | 2008 | Science China Mathematics2008，51，2： | 2 |
| 2 | LIL behavior for B-valued strong mixing random variables显示文摘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. | FU KeAng ZHANG LiXin | 2011 | Science China Mathematics2011，54，4： | 1 |
| 3 | ASYMPTOTICS FOR THE DISTRIBUTION FUNCTION ESTIMATORS OF THE ERRORS IN SEMI-PARAMETRIC REGRESSION MODELS显示文摘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. | QIU Yuyang FU Keang HUANG Wei | 2014 | Journal of Systems Science & Complexity2014，27，2： | 0 |
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