多组样本下GL—统计量的渐近性质

本文主要讨论多组样本下GL－统计量的渐近分布,这里我们使用了Gateaut微分逼近方法,在多组i.i.d.样本下,给出了GL－统计量的渐近正态分布的一组条件,从而拓广了i.i.d样本下GL－统计量的渐近正态分布的性质[1]。     

相协样本下Wilcoxon两样本统计量的渐近分布北大核心CSCD

研究了相协样本下Wilcoxon两样本统计量的渐近分布的问题.利用Hoeffding分解方法,获得了相协样本下Wilcoxon两样本统计量的渐近分布为正态分布的结果,推广了负相协样本下Wilcoxon两样本统计量的渐近分布的结果.     

相协样本下Wilcoxon两样本统计量的渐近分布

研究了相协样本下Wilcoxon两样本统计量的渐近分布的问题.利用Hoeffding分解方法,获得了相协样本下Wilcoxon两样本统计量的渐近分布为正态分布的结果,推广了负相协样本下Wilcoxon两样本统计量的渐近分布的结果.     

正态密度比的假设检验

本文讨论对两样本正态分布密度比的假设检验.给出了基于统计量渐近正态性的大样本检验和广义$p$-值检验并给出了广义$p$-值检验的一些频率性质.模拟表明广义$p$-值检验在小样本情形下的表现优于大样本检验.     

双边截断情形下QH 统计量的渐近分布

ＣｈｅｎＬａｎｄＳｈａｐｉｒｏＳＳ［１］提出如下检验正态性的统计量其中,Ｘ１ｎ,Ｘ２ｎ,…,Ｘｎｎ为容量为n的样本的次序统计量,Ｈ为标准正态分布函数的逆函数．本文在一定的条件下得到了双边截断情形下ＱＨ统计量的渐近分布．     

关于线性秩统计量的渐近正态性及其收敛速度

本文讨论线性秩统计量的渐近正态性的条件及其收敛速度．推广了Hajek关于线性秩统计量收敛于正态分布的条件的重要定理，并得出了一个较易验证的充分条件．对于一般形式的计分函数，在一定条件下得出了相应线性秩统计量收敛于正态分布的速度．     

球面均匀分布的拟合优度检验

证明了基于惯量矩的d维单位球面上样本服从均匀分布的基本特征,得到球面均匀分布协差阵特征根估计的强相合性及渐近多元正态性.提出了检验球面上样本均匀性的渐近卡方统计量,证明了拟合优度检验的相合性并做检验功效的随机模拟.     

φ-混合样本下有限个分位数估计的联合渐近分布

本文研究了φ-混合样本下总体的有限个分位数核估计的渐近性质.利用分块技术证明了φ-混合样本下总体的有限个分位数核估计的联合渐近分布为多元正态分布,推广了文献[16]的相关结果.     

关于高斯随机游动之Shepp统计量的极值的一些渐近结果（英文）

设{x_i∶i≥1}是一列独立的标准化的服从正态分布的随机变量序列,令S_k=∑_(i=1)~kX_i,S_0=0为相关的高斯随机游动.当T是一正的独立于{X_i∶i≥1}的随机变量时,获得了Shepp统计量之极值M_T~(N)=max(k+L-1)-S_(k-1))的尾渐近展开.同时也证明了M_T~(N)的几乎处处极限定理.     

相协样本下密度核估计的联合渐近分布

证明了相协样本下密度函数的核估计在有限个不同点上的联合渐近分布为多维正态分布.     

Probabilistic analysis of a differential equation for linear programming

In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are i.i.d. Gaussian variables, we compute the distribution of the convergence rate to the attracting fixed point. Using the framework of Random Matrix Theory, we derive a simple expression for this distribution in the asymptotic limit of large problem size. In this limit, we find the surprising result that the distribution of the convergence rate is a scaling function of a single variable. This scaling variable combines the convergence rate with the problem size (i.e., the number of variables and the number of constraints). We also estimate numerically the distribution of the computation time to an approximate solution, which is the time required to reach a vicinity of the attracting fixed point. We find that it is also a scaling function. Using the problem size dependence of the distribution functions, we derive high probability bounds on the convergence rates and on the computation times to the approximate solution.     

Estimating generalized state density of near-extreme events and its applications in analyzing stock data

This paper studies the generalized state density (GDOS) of near-historical extreme events of a set of independent and identically distributed (i.i.d.) random variables. The generalized density of states is proposed which is defined as a probability density function (p.d.f.). For the underlying distribution in the domain of attraction of the three well-known extreme value distribution families, we show the approximate form of the mean GDOS. Estimates of the mean GDOS are presented when the underlying distribution is unknown and the sample size is sufficiently large. Some simulations have been performed, which are found to agree with the theoretical results. The closing price data of the Dow-Jones industrial index are used to illustrate the obtained results.     

Multilevel Monte Carlo in approximate Bayesian computation

In the following article, we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.     

Equality of Types for the Distribution of the Maximum for Two Values of n Implies Extreme Value Type

In this note, we prove a characterization of extreme value distributions. We show that, under some conditions, if the distribution of the maximum of n i.i.d. variables is of the same type for two distinct values of n then the distribution is one of the three extreme value types. This is an analogue of the well known result that if the sum of two i.i.d. random variables with finite second moment is of the same type as the original distribution then the distribution is Gaussian (Kagan et al., 1973). Our result was motivated by study of the m out of n bootstrap.     

高维正态概率积分的降维算法与L_1逼近

高维正态概率积分计算一直是统计学家关注的课题．早期工作已由Gupta（1963）[1]评价，并给出大量的参考文献．近期工作则可参考Tong（1990）[2]的专著．虽然有关的文献很多，但是除了二、三维问题已有较好的算法外（例如见Zhana－Yana，1993[3]），更高维问题尚无公认的有效算法．在维数m＞3的高维情形，多数文章常假设积分域或相关阵有特殊形式，否则只有使用MonteCarlo方法［4］或拟MonteCarlo方法（亦称数论网格方法，例如见Fang－Wang，1994[5]）．但即使是被认为较好的拟MonteCarlo方法，其收敛阶仅为O（n－2／m），因此对于真…     

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??Kolmogorov-Smirnov (KS), Cramer-von Mises (CM) and Anderson-Darling (AD) test, which are based on empirical distribution function (EDF), are well-known statistics in testing univariate normality. In this paper, we focus on the high dimensional case and propose a family of generalized EDF based statistics to test the high-dimensional normal distribution by reducing the dimension of the variable. Not only can we approximate the corresponding critical values of three statistics by Monte Carlo method, we also can investigate the approximate distributions of proposed statistics based on approximate formulas in univariate case under null hypothesis. The Monte Carlo simulation is carried out to demonstrate that the performance of proposed statistics is more competitive than existing methods under some alternative hypotheses. Finally, the proposed tests are applied to real data to illustrate their utility.     

Approximations for the Boundary Crossing Probabilities of Moving Sums of Random Variables

Methodology and Computing in Applied Probability - In this paper we study approximations for the boundary crossing probabilities of moving sums of i.i.d. normal random variables. We approximate a...     

A new approach to the credibility formula

The usual credibility formula holds whenever, (i) claim size distribution is a member of the exponential family of distributions, (ii) prior distribution conjugates with claim size distribution, and (iii) square error loss has been considered. As long as, one of these conditions is violent, the usual credibility formula no longer holds. This article, using the mean square error minimization technique, develops a simple and practical approach to the credibility theory. Namely, we approximate the Bayes estimator with respect to a general loss function and general prior distribution by a convex combination of the observation mean and mean of prior, say, approximate credibility formula. Adjustment of the approximate credibility for several situations and its form for several important losses are given.     

Extremes of independent chi-square random vectors

We prove that the componentwise maximum of an i.i.d. triangular array of chi-square random vectors converges in distribution, under appropriate assumptions on the dependence within the vectors and after normalization, to the max-stable Hüsler–Reiss distribution. As a by-product we derive a conditional limit result.     

带约束条件集值优化问题近似Henig有效解集的连通性

研究了带约束条件集值优化问题近似Henig有效解集的连通性.在实局部凸Hausdorff空间中,讨论了可行域为弧连通紧的,目标函数为C-弧连通的条件下,带约束条件集值优化问题近似Henig有效解集的存在性和连通性.并给出了带约束条件集值优化问题近似Henig有效解集的连通性定理.