Operator stable laws: Series representations and domains of normal attraction

LetX,X ₁,X ₂,... be i.i.d. random vectors in ^d. The limit laws that can arise by suitable affine normalizations of the partial sums,S _n=X ₁+...+X _n, are calledoperator-stable laws. These laws are a natural extension to ^d of the stable laws on. Thegeneralized domain of attraction of [GDOA()] is comprised of all random vectorsX whose partial sums can be affinely normalized to converge to . If the linear part of the affine transformation is restricted to take the formn ^–B for some exponent operatorB naturally associated to thenX is in thegeneralized domain of normal attraction of [GDONA()]. This paper extends the theory of operator-stable laws and their domains of attraction and normal attraction.     

Limit distribution of the coefficients of polynomials with only unit roots

We consider sequences of random variables whose probability generating functions have only roots on the unit circle, which has only been sporadically studied in the literature. We show that the random variables are asymptotically normally distributed if and only if the fourth central and normalized (by the standard deviation) moment tends to 3, in contrast to the common scenario for polynomials with only real roots for which a central limit theorem holds if and only if the variance is unbounded. We also derive a representation theorem for all possible limit laws and apply our results to many concrete examples in the literature, ranging from combinatorial structures to numerical analysis, and from probability to analysis of algorithms. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46,707–738, 2015     

中国经济随机前沿模型效率的贝叶斯统计推断

基于扩展的随机生产前沿模型,研究了区域生产效率的差异和其影响因素的作用效果,应用贝叶斯统计方法对中国各省份2010-2017的年度数据(不包含港澳台地区,下同)进行了实证研究.研究发现:生产效率总体呈逐渐下降的趋势,地区间生产效率有一定的差异,高等教育规模对生产效率具有显著的直接影响.人力资本能有效促进东部和中部地区的经济增长,西部地区主要依靠资本促进经济增长.环境污染对中部地区的经济增长具有一定的负向作用.     

2008年欧洲足球锦标赛攻击性进攻技术统计分析

采用专家调查、录像观察和数理统计等研究方法,从训练学角度探讨2008年欧锦赛攻击性进攻的现状。每个国家都适当选择了运球突破,每场突破的次数主要集中在15-18之间,并且P值显示出明显的差异性;西班牙、荷兰、德国和葡萄牙表现突出,多采用中距离传球;比赛成绩(排名)与进球的相关系数为-0.597,且其差异性显著;角球攻击的区域90%集中在1区和2区,而且1区的攻击多于2区;长传279次、短传37次,T=9.76、P=0.00(?)0.01,二者之间存在明显的差异性;运用内弧线球和外弧线球平均次数之间差异不具有显著性。研究认为:运球突破的实效性、传球的成功率、射门的准确性和攻击性控球的把握是决定比赛胜利的关键。     

A New Method for Estimating the Distribution of Scan Statistics for a Two-Dimensional Poisson Process

A method for estimating the distribution of scan statistics with high precisìon was introduced in Haiman (2000). Using that method sharp bounds for the errors were also established. This paper is concerned with the application of the method in Haiman (2000) to a two-dimensional Poisson process. The method involves the estimation by simulation of the conditional (fixed number of points) distribution of scan statistics for the particular rectangle sets of size 2 × 2, 2 × 3, 3 × 3, where the unit is the (1 × 1) dimension of the squared scanning window. In order to perform these particular estimations, we develop and test a perfect simulation algorithm. We then perform several numerical applications and compare our results with results obtained by other authors.     

Asymptotic Bound on the Characteristic Function of Signed Linear Serial Rank Statistics

This work establishes an asymptotic bound on the characteristic function of signed linear serial rank statistics. The result is obtained under rather general conditions including the important case of van der Waerden scores. It generalizes the result of Seoh (1983, Ph.D. Thesis, Department of Mathematics, Indiana University) and constitutes an essential step to the elaboration of Berry-Esséen's bounds and the establishment of Edgeworth expansions. These statistics constitute a natural tool for testing the hypothesis of white noise with a symmetrical (unspecified) distribution in comparison to other alternative hypothesis of serial dependence.     

An optimization approach to adaptive multi-dimensional capital management

Firms should keep capital to offer sufficient protection against the risks they are facing. In the insurance context methods have been developed to determine the minimum capital level required, but less so in the context of firms with multiple business lines including allocation. The individual capital reserve of each line can be represented by means of classical models, such as the conventional Cramér–Lundberg model, but the challenge lies in soundly modelling the correlations between the business lines. We propose a simple yet versatile approach that allows for dependence by introducing a common environmental factor. We present a novel Bayesian approach to calibrate the latent environmental state distribution based on observations concerning the claim processes. The calibration approach is adjusted for an environmental factor that changes over time. The convergence of the calibration procedure towards the true environmental state is deduced. We then point out how to determine the optimal initial capital of the different business lines under specific constraints on the ruin probability of subsets of business lines. Upon combining the above findings, we have developed an easy-to-implement approach to capital risk management in a multi-dimensional insurance risk model.     

我国证券市场风险计量模型的构建

证券风险的计量准确与否,是证券组合理论能否有效运用的前提,在现有研究成果的基础上,结合我国证券市场的特点,选取“流通市值”作为影响我国证券风险的第二个因素,建立了证券风险计量模型,并使用统计软件对模型的适用性进行了检验．     

1996～2000年《武汉大学学报(自然科学版)》引文分析

以1996-2000年《武汉大学学报（自然科学版）》上发表的917篇科技论文为统计样本，据义献计量学的方法对其引文进行了统计分析．结果表明：《武汉大学学报（自然科学版）》篇均引文节为7．83，引文主要类型为期刊。占76．6％。外文文献占引文总数的66．77％，最大中文引文年限为2年，半哀期为7年，衰减系数为31．30％．最大外义引文年限为3年，半哀期为10年，哀减系数为17．08％．刊载论文的总被引量和总影响因子在逐年增加。