Ornstein-Uhlenbeck过程参数估计的渐近正态性

利用Wick引理研究并得到了OU过程的非负参数估计的渐近正态性.     

Testing serial correlation in semiparametric varying coefficient partially linear errors-in-variables model

The authors propose a V _{N, p} test statistic for testing finite-order serial correlation in a semiparametric varying coefficient partially linear errors-in-variables model. The test statistic is shown to have asymptotic normal distribution under the null hypothesis of no serial correlation. Some Monte Carlo experiments are conducted to examine the finite sample performance of the proposed V _{N, p} test statistic. Simulation results confirm that the proposed test performs satisfactorily in estimated size and power. This research is supported by the National Natural Science Foundation of China under Grant Nos. 10871217 and 40574003; the Science and Technology Project of Chongqing Education Committee under Grant No. KJ080609; the Doctor's Start-up Research Fund under Grant No. 08-52204; and the Youth Science Research Fund of Chongqing Technology and Business University under Grant No. 0852008.     

涉及微分多项式的亚纯函数正规性

研究了涉及微分多项式的亚纯函数的正规性.继承Schwick的思想将正规族与分担值联系起来,对一族亚纯函数中函数与该函数微分多项式分担值的情况进行研究,得出亚纯函数的正规性.已知定理:设F为区域D上的全纯函数族,k为正整数,a,b,c和d为有穷复数,b≠0,c≠0且b≠a,若对f∈F,f-d的零点重级至少为k,f=0f(k)=a且f(k)=bf=c. 则F在D上正规.本文将这个定理推广到亚纯函数情形,并且将f(k)用f的微分多项式来代替,结论仍成立.     

分担小函数的亚纯函数的正规族

文章主要运用Zalcman引理证明了区域D上的一族亚纯函数R,分担D上的非零解析函数a（z）,如果满足对任意的f∈Rf的零点重级至少为k＋1,若f^（k）=0=〉f=0,并且f^（k）（z）=a（z）=〉f（z）=a（z）,则有R在区域D上正规．     

一类具有渐近正态的统计量的随机加权逼近

对一类具有渐近正态的统计量 ,找到了适用于它们的共同的随机加权逼近方法 ,并研究了它的相合性、一致及非一致逼近速度     

线性统计模型中回归分位点的强相合性及渐近正态性(英文)

论证了线性模型中回归分位点估计量的强相合性及渐近正态性等大样本性质 ,这些结果推广了陈希孺等 ( 1 990 ,1 992 )的有关定理 ,改进了Koenker与Basstee( 1 978) ,Gutenburnner与Jurec∨kova( 1 992 ) ,以及Jurec∨kovo与Prochazka( 1 994)等人的有关成果。     

关于截尾数据半参数回归模型的估计理论的一点注记

文[1]研究了截尾情形征半参数回归模型中未知参数及函数的估计问题,得到了它们的大样本性质。本文对这个问题作了进一步的研究,去掉了文[1]中某些过强的条件并改进了部分结论。     

RDSA算法最优的随机方向

给出了RDSA算法的渐近正态性，讨论了在两个标准下此算法的最优的随机方向。     

由高斯移动平均过程驱动的一类随机微分方程的极大似然估计

在高斯移动平均过程是半鞅情况下,研究由其驱动的随机微分方程的极大似然估计获得了渐近一致的估计,并证明了该估计量的强相容性和渐近正态性,从而推广了经典情形下的相应结果.     

ASYMPTOTIC NORMALITY OF SOME ESTIMATORS IN A FIXED-DESIGN SEMIPARAMETRIC REGRESSION MODEL WITH LINEAR TIME SERIES ERRORS

Consider a semiparametric regression model with linear time series errors Yk = x'kβ g(tk) εk, 1 < k < n, where Yk's are responses, xk = (xk1,xk2,..... ,xkp)' and tk ∈T ∪R are fixed design points, β= (β1, β2, ....., βp)' is an unknown parameter vector, g(.) is an unknown bounded real-valued function defined on a compact subset T of the real line R, and εk is a linear process given by εk = ∑j=0∞j(?)ek-j,(?)= 1, where , are i.i.d. random variables. In this paper we establish the asymptotic normality of the least squares estimator of β, a smooth estimator of g(.), and estimators of the autocovariance and autocorrelation functions of the linear process εk.