Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship

Here we study the problems of local asymptotic normality of the parametric family of distributions and asymptotic minimax efficient estimators when the observations are subject to right censoring. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and furthermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.     

关于离散型随机变量次序统计量分布矩阵对称性猜想的探索

本文研究了离散型随机变量次序统计量的分布矩阵的对称性 ,获得了二个定理 .定理 1　服从等概率二点分布或等概率三点分布的离散型随机变量的次序统计量的分布矩阵是对称矩阵 .定理 2　取值有限且等概率的离散型随机变量的次序统计量的分布矩阵具有中心对称性 .     

INS／GPS／SAR组合系统白噪声误差特性的在线随机加权估计

首次把随机加权估计这一新兴的统计计算方法应用于导航系统的研究,证明用它进行INS/GPS/SAR组合系统误差特性的估计是可行的,仿真实验和计算结果表明,该方法明显地优于其它传统的统计估计方法。     

A supplement to precise asymptotics in the law of the iterated logarithm

Let be a sequence of real-valued i.i.d. random variables with E(X)=0 and E(X²)=1, and set , n?1. This paper studies the precise asymptotics in the law of the iterated logarithm. For example, using a result on convergence rates for probabilities of moderate deviations for obtained by Li et al. [Internat. J. Math. Math. Sci. 15 (1992) 481-497], we prove that, for every b∈(−1/2,1],

     

Co-countable sets of uniqueness for series of independent random variables

Given a sequence of independent random variables (fk) on a standard Borel space Ω with probability measure μ and a measurable set F, the existence of a countable set S⊂F is shown, with the property that series k_∑ckfk which are constant on S are constant almost everywhere on F. As a consequence, if the functions fk are not constant almost everywhere, then there is a countable set S⊂Ω such that the only series k_∑ckfk which is null on S is the null series; moreover, if there exists b<1 such that for every k and every α, then the set S can be taken inside any measurable set F with μ(F)>b.     

Kubilius-Type Sequences of Additive Functions

We consider conditions under which the distributions of sequences of integer-valued nonnegative strongly additive functions can be approximated by the distributions of sums of independent random variables.__________Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 2, pp. 270–281, April–June, 2005.     

离散随机变量序列的强偏差定理

利用分析方法建立了用不等式表示的用对数似然比刻划的任意相依离散随机变量序列的强偏差定理,作为推论得到了更一般的离散随机变量序列加权和的强大数定律.     

两两PQD序列的完全收敛性和强大数定律

给出两两PQD序列部分和的几个不等式,研究了一类广泛的随机变量序列两两PQD列的收敛性质,得到了与PA序列相类似的完全收敛性和强大数定律的结果.     

一类奇摄动微分——差分反应扩散方程

奇摄动问题有很强的自然科学的背景,它在生态环境、大气物理、海洋科学、催化反应、激波和量子物理中都有很广泛的应用.本文研究了一类带有小延迟的微分--差分反应扩散方程初值问题.在适当的条件下,利用奇摄动伸长变量法,构造了问题的形式渐近解.再用微分不等式理论证明了解的一致有效性.