Poisson approximation io the distribution of empiy cells in randomized occupancy

Let M_o denote the number of empty cells when n balls are dropped independently and at random in m cells such that each ball stays in its cell with probability p and falls through with probability 1-p. A Poisson limit is known for M_o when (n/m)→∞. We find a corresponding approximation to the distribution of M_o when m is large but finite, Ihe method is elementary, and yields the rate of convergence to the limit law. Ihe results are new for the classical case (p = 1) as well.     

Convergence in weighted supremum norms of the skorokhod representation of the estimated empirical process

Anderson and Darling (1952) introduced their test with a weight function which is the reciprocal of the variance of the empirical process. The fact that this weight function is not integrable was a source of problems, and in spite of the large amount of works that have been done there is no a rigorous proof of the asymptotic distribution of the Anderson-Darling statistics when the parameters are estimated.     

Naive method to test the convergence of simulation and its applications in the computation of bankruptcy probability

We analyse a naive method using sample mean and sample variance to test the convergence of simulation. We find this method is valid for identically, independently distributed samples, as well as correlated samples with correlation disappearing in long period. Our simulation results on the approximation to bankruptcy probability (BP) show the naive method compares well with the Half-Width, Geweke and CUSUM methods in terms of accuracy and time cost. There are clear evidences of variance reduction from tail-distribution sampling for all convergence test methods when the true BP is very low.     

Penalized pseudo-likelihood hazard estimation: A fast alternative to penalized likelihood

Penalized likelihood method has been developed previously for hazard function estimation using standard left-truncated, right-censored lifetime data with covariates, and the functional ANOVA structures built into the log hazard allows for versatile nonparametric modeling in the setting. The computation of the method can be time-consuming in the presence of continuous covariates; however, due to the repeated numerical integrations involved. Adapting a device developed by Jeon and Lin [An effective method for high dimensional log-density ANOVA estimation, with application to nonparametric graphical model building. Statist. Sinica 16, 353–374] for penalized likelihood density estimation, we explore an alternative approach to hazard estimation where the log likelihood is replaced by some computationally less demanding pseudo-likelihood. An assortment of issues are addressed concerning the practical implementations of the approach including the selection of smoothing parameters, and extensive simulations are presented to assess the inferential efficiency of the “pseudo” method as compared to the “real” one. Also noted is an asymptotic theory concerning the convergence rates of the estimates parallel to that for the original penalized likelihood estimation.     

大规模网络虚拟戏剧中的模仿聚合

基于网络的虚拟戏剧是一种建立在互联网基础上的交互式虚拟戏剧平台。这种虚拟戏剧模型不同于传统虚拟戏剧的＂独立封闭＂形式,该模型将虚拟戏剧场景分布在网络中的不同电脑上;每个参与人通过Agent提出自己的戏剧场景,并且与电脑上其他参与人的Agent进行交互协同。在大规模网络虚拟戏剧中,Agent之间为了实现统一的戏剧情节或者场景,通常会模仿与其有交互关系的其他Agent的行为策略,从而最终实现整个网络系统内的戏剧情节的聚合。本文主要研究了三种典型的模仿聚合方式：基于趋同权威的模仿聚合;基于趋众行为的模仿聚合;基于好感度的模仿聚合。     

On the error term in bahadur's representation of an order statistic

Bahadur (1966) presented a representation of an order statistic, giving its asymptotic distribution and the rate of convergence, under weak assumptions on the density function of the parent distribution. In this paper we consider the mean(squared) deviation of the error term in Bahadur’s approximation of the q th sample quantile (q_n ). We derive a uniform bound on the mean (squared) deviation of q_n , not depending on the value of q. An application of the given result provides the corresponding result for a kernel type estimator of the q th quantile.     

Empirical bayes estimation of binomial parameter with symmetric priors

This paper deals with the problem of estimating the binomial parameter via the nonparametric empirical Bayes approach. This estimation problem has the feature that estimators which are asymptotically optimal in the usual empirical Bayes sense do not exist (Robbins (1958, 1964)), However, as pointed out by Liang (1934) and Gupta and Liang (1988), it is possible to construct asymptotically optimal empirical Bayes estimators if the unknown prior is symmetric about the point 1/2, In this paper, assuming symmetric priors a monotone empirical Bayes estimator is constructed by using the isotonic regression method. This estimator is asymptotically optimal in the usual empirical Bayes sense. The corresponding rate of convergence is investigated and shown to be of order n^-1, where n is the number of past observations at hand.     

略论俄罗斯各级各类高等教育的衔接与沟通——基于课程与制度的视角

随着高等教育的日趋多元化,各级各类高等教育间的衔接与沟通就显得尤为重要了。从俄罗斯两大层级高等教育(5级和6级)的衔接以及两大类型高等教育(5A和5B)的沟通来看,在俄罗斯高等教育体系中,普通高等教育和高等职业教育并存,分工明确,相互协作,形成四通八达的人才成长立交桥,使得整个高等教育学制貌似分支型,实质上却融为一体,近似单轨型。     

互联网环境下基于集中管理模式的数字版权自动许可与补偿制度

随着互联网经济的飞速发展,传统的许可申请——授权的版权制度模式已经逐渐不能满足知识传播以及合理使用的需要。基于国外版权补偿制度的理论基础,结合中国实际构想并设计了一种数字版权自动许可——下载——收费补偿的模式,真正实现数字的版权的集中管理与自动授权许可,通过此制度与系统可以较好地协调数字版权人的私权利与互联网2.0体系下知识传播与共享之间的价值平衡。     

Adaptive fitting of linear mixed-effects models with correlated random effects

Linear mixed-effects model has been widely used in longitudinal data analyses. In practice, the fitting algorithm can fail to converge due to boundary issues of the estimated random-effects covariance matrix G, that is, being near-singular, non-positive definite, or both. Current available algorithms are not computationally optimal because the condition number of matrix G is unnecessarily increased when the random-effects correlation estimate is not zero. We propose an adaptive fitting (AF) algorithm using an optimal linear transformation of the random-effects design matrix. It is a data-driven adaptive procedure, aiming at reducing subsequent random-effects correlation estimates down to zero in the optimal transformed estimation space. Simulations show that AF significantly improves the convergent properties, especially under small sample size, relative large noise and high correlation settings. One real data for insulin-like growth factor protein is used to illustrate the application of this algorithm implemented with software package R (nlme).