Optimal allocation for estimating the correlation coefficient of Morgenstern type bivariate exponential distribution by ranked set sampling with concomitant variable

Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on the auxiliary variable X which is correlated with the study variable Y, where (X, Y) follows Morgenstern type bivariate exponential distribution. The authors discuss the optional allocation for unbiased estimators of the correlation coefficient ρ of the random variables X and Y when the auxiliary variable X is used for ranking the sample units and the study variable Y is measured for estimating the correlation coefficient. This paper first gives a class of unbiased estimators of ρ when the mean θ of the study variable Y is known and obtains an essentially complete subclass of this class. Further, the optimal allocation of the unbiased estimators is found in this subclass and is proved to be Bayes, admissible, and minimax. Finally, the unbiased estimator of ρ under the optimal allocation in the case of known θ is reformed for estimating ρ in the case of unknown θ, and the reformed estimator is shown to be strongly consistent.     

Cross-Entropy Minimization Estimation for Two-Phase Sampling and Non-Response

This paper considers the problem of estimating the finite population total in two-phase sampling when some information on auxiliary variable is available.The authors employ an informationtheoretic approach which makes use of effective distance between the estimated probabiUties and the empirical frequencies.It is shown that the proposed cross-entropy minimization estimator is more efficient than the usual estimator and has some desirable large sample properties.With some necessary modifications,the method can be applied to two-phase sampling for stratification and non-response.A simulation study is presented to assess the finite sample performance of the proposed estimator.     

ON A CLASS OF ANISOTROPIC DIFFUSION EQUATIONS

ＯＮＡＣＬＡＳＳＯＦＡＮＩＳＯＴＲＯＰＩＣＤＩＦＦＵＳＩＯＮＥＱＵＡＴＩＯＮＳＯＮＡＣＬＡＳＳＯＦＡＮＩＳＯＴＲＯＰＩＣＤＩＦＦＵＳＩＯＮＥＱＵＡＴＩＯＮＳ￥ＧＡＯＨａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔ...     

用信息扩散模型改进台风风险估计

频繁且随机发生的台风,其风险是概率风险,具有统计学的意义.用历史台风的损失记录作为样本来量化风险时,台风风险就是台风损失样本的平均值,它必等于由台风发生概率和易损性偶合估计出的损失期望值.当统计资料较少时,由于信息扩散模型能提高小样本的工作效率,消除用简单统计方法估计风险时出现的平缓和跳空现象,较好地表现统计规律,从而能改进台风风险的估计精度.按年分段形成的多个样本函数可用于计算物理意义明确的台风年度风险值,并可用信息扩散模型对其加以改进.蒙特卡罗法并不具有改进风险评估精度的功能.本文以浙江省部分历史台风资料为样本,演示了台风风险的估计.信息扩散模型的改进程度如何,将另文用计算机仿真的方法来加以检验.     

An Efficient Multiple Imputation Approach for Estimating Equations with Response Missing at Random and High-Dimensional Covariates

Empirical-likelihood-based inference for parameters defined by the general estimating equations of Qin and Lawless(1994) remains an active research topic. When the response is missing at random(MAR) and the dimension of covariate is not low, the authors propose a two-stage estimation procedure by using the dimension-reduced kernel estimators in conjunction with an unbiased estimating function based on augmented inverse probability weighting and multiple imputation(AIPW-MI) methods. The authors show that the resulting estimator achieves consistency and asymptotic normality. In addition, the corresponding empirical likelihood ratio statistics asymptotically follow central chi-square distributions when evaluated at the true parameter. The finite-sample performance of the proposed estimator is studied through simulation, and an application to HIV-CD4 data set is also presented.     

常微分方程初值问题并行算法研究现状

本文对常微分方程初值问题数值求解的并行算法进行综述,给出并行算法的应用前景和构造的一些途径,同时指出并行化的主要困难和一些解决的方法。     

风险度量半参数变系数复合Expectile回归模型及应用

本文结合半参数变系数回归模型、期望分位数风险价值(EVaR)的思想以及充分利用多个Expectile信息能提高参数估计效率的假设,提出了一类半参数变系数复合Expectile回归模型,并对该模型进行了估计,建立了所提出复合Expectile回归(CER)估计的大样本性质.针对该模型既含有参数部分也含有非参数部分的特征,采用了方便计算的三步估计方法.通过数值模拟也发现,当误差为厚尾或非对称分布时,在均方根误差(RMSE)的标准下,所提出的CER估计大大优于最小二乘(LS)估计和简单的Expectile回归(ER)估计.另外,本文还应用所发展的理论分析了我国货币政策对上证综指的影响.     

The Blowing-up of the Solutions for a Class of Nonlinear Reaction-Diffusion Equations

Wediscusstheblowing-upofthesolutionsforthenonlinearreaction-diffusionequationswiththegeneral(i.e.nonlinear)boundaryconditions:ut=∑ni,j=1xiaij(x)uxj ∑ni=1bi(x)uxi f(u)　(x,t)∈Ω×(0,T)βuγ δ(x)uΩ=g(u)u(x,0)=u0(x)(*)whereΩisaboundedregionofRn,ai...     

A Class of Jump-Diffusion Stochastic Differential System Under Markovian Switching and Analytical Properties of Solutions

Our article discusses a class of Jump-diffusion stochastic differential system under Markovian switching(JD-SDS-MS). This model is generated by introducing Poisson process and Markovian switching based on a normal stochastic differential equation. Our work dedicates to analytical properties of solutions to this model. First, we give some properties of the solution, including existence,uniqueness, non-negative and global nature. Next, boundedness of first moment of the solution to this model is considered. Third, properties about coefficients of JD-SDS-MS is proved by using a right continuous markov chain. Last, we study the convergence of Euler-Maruyama numerical solutions and apply it to pricing bonds.     

Valuation of stock loans under a Markov chain model

In recent years the use of Markov chain models to model stock price movement has received increased attention among researchers. Markov chain models combine the discrete movements of a binomial tree model while retaining the Markovian properties of Brownian motion, thus allowing the best properties of both of these models. In this paper, the authors consider a Markov chain model in which the underlying market is solely determined by a two-state Markov chain. Such a Markov chain model is strikingly simple and yet appears capable of capturing various market movements. By proper selection of parameters, the Markov chain model can produce sample paths that are very similar to or very distinct from a classical Brownian motion, as the authors demonstrate in this paper. This paper studies the stock loan valuation, or the value of a loan in which a risky share of stock is used as collateral, under such a model. Dynamic programming equations in terms of variational inequalities are used to capture the dynamics of the problem. These equations are solved in closed-form. Explicit optimal solutions are obtained. Numerical examples are also reported to illustrate the results.     

BOUNDARY SOLUTIONS OF OPERATOR EQUATIONS IN PARIAL ORDERING SETS WITH APPLICATIONS TO SYSTEMS OF FUNCTIONAL

1.IntroductionThepaPers[l-5]studythecoupledfixedp0intsofmixedmonotoneoperatorsinBanachspaces;theyshowusgeneralizationsofthefixedpoillttheoremsonincreasingoperatorsanddecreasingoperators.Applicationsoftheseresultsmaybefoundinmanyfieldsofmathematicssuchasnonlineaxdifferentialequations,illtegralequationsanddynamicprogrammingtheories.Inthispaper,westudytheekistenceofsolutionsandboundarysolutionstoasystem0foperatorequationsinpartialorderingsets.Wegeneralizeandimproveonsomeresultsaboutthecoupledfix…     

Equations of Fuzzy Criterion Models for Reservoir Operations

In this paper we discuss the equations of fuzzy criterion models for reservoir operations based on dynamic programming. The continuity, existence, uniqueness and stability of solutions are shown under some conditions.     

仿真输出分析中的BAYES方法

本文提出用Bayes方法对小样本或单次运行的仿真输出进行分析。给出了几种条件下的Bayes方法和伽玛分布置信区间的估计方法。并用M/M/I排队系统对几种方法进行了实例研究。实验结果表明,在处理小样本或单次仿真运行时Bayes方法有明显的优越性和应用前景。     

Efficient estimation of seemingly unrelated additive nonparametric regression models

This paper is concerned with the estimating problem of seemingly unrelated (SU) nonparametric additive regression models. A polynomial spline based two-stage efficient approach is proposed to estimate the nonparametric components, which takes both of the additive structure and correlation between equations into account. The asymptotic normality of the derived estimators are establishedi. The authors also show they own some advantages, including they are asymptotically more efficient than those based on only the individual regression equation and have an oracle property, which is the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedure. Applying the proposed procedure to a real data set is also made.     

NON-CLASSICAL GENERALIZED SOLUTIONS FOR SOME HYPERBOLIC SYSTEMS

1.IntroductionThemostspecialfeatureofconservationlawsofhyperbolicsystemsisthattheirsolutionsalwayshavediscolltinuities.ThiskindofdiscontinuityrepresentstheshoCkwavephenomena.Sopeopleintroducetheideaofgeneralizedsolutionwhichsatisfiesequationsinthesenseofdistribution.Underthisdefinition,alotofachievementshavebeenobtainedsince1950'sinthisfield.However,inrecelltyears,manyauthors(see[l--6])discoveredthatthereisnoexistenceanduniqllenessofsolutionstoRiemannproblemsforsomeconservationlaws.Bynumeric…     

Study on Variation of Parameters Formula and Stability for Impulsive Time－Delay Nonlinear Large Scale Systems

ＳｔｕｄｙｏｎＶａｒｉａｔｉｏｎｏｆＰａｒａｍｅｔｅｒｓＦｏｒｍｕｌａａｎｄＳｔａｂｉｌｉｔｙｆｏｒＩｍｐｕｌｓｉｖｅＴｉｍｅ－ＤｅｌａｙＮｏｎｌｉｎｅａｒＬａｒｇｅＳｃａｌｅＳｙｓｔｅｍｓＧＵＡＮＺｈｉｈｏｎｇ（Ｄｅｐｔ．ｏｆＢａｓｉｃＳｃｉｅｎｃ...     

基于HKKP估计的商业银行操作风险估计

对于商业银行而言，操作风险已经成为与市场风险和信用风险同样重要的风险。本文利用极值理论对中国商业银行操作损失极端值分布进行估计，针对尾参数估计的采用传统Hill估计对小样本数据容易产生偏倚的情况，提出了采用Hill估计的改进——小样本无偏估计的HKKP估计来估计操作损失的尾参数，针对由于阈值确定不准确导致结果偏差大的情况，采用最小化估计的累计概率分布与经验累计概率分布平均平方误差的方法确定较精确的阈值，估计出给定置信水平下操作风险损失的分位数，从而使得中国商业银行操作风险监管资本的测定成为可能。     

结合样本分割与系统方程的稳健性统计检验方法

结合二元样本分割与系统方程方法,提出一种新的稳健性统计检验.首先建立理论模型,分析结构方程模型中条件外生性假设与参数解释的关系,确定备择模型的构建原则;接着提出混淆变量调整与二元样本分割两种备择模型构建方法;最后基于系统方程方法建立假设检验,并针对奇异性问题改进检验统计量.蒙特卡罗实验表明,本文的稳健性统计检验具有良好的小样本表现.以Acemoglu教授关于人口老龄化与经济增长的研究为例,应用本文方法进行检验,发现该研究的部分模型存在误设问题.     

用于组合有效性综合评价的非参数方法研究

针对系统内部同类单元的联合问题,给出了一类基于样本数据评价组合有效性的非参数模型和方法,并探讨了评价组合有效性模型的性质、求解方法以及模型给出的组合有效性的经济含义。分析了组合有效单元与相应的多目标规划Pareto有效解之间的关系,探讨了外界条件变化对评价结果的影响。为了进一步在模型中反映决策者的偏好,给出了带有权重约束的评价组合有效性模型,并探讨了其相关性质。     

An Additive-Multiplicative Cox-Aalen Subdistribution Hazard Model for Competing Risks Data

This paper proposes a flexible additive-multiplicative Cox-Aalen hazard model which allows time-varying covariate effects for the subdistribution in a competing risks study. Weighted estimating equation approaches under an covariates-dependent adjusted weight by fitting the Cox proportional hazard model for the censoring distribution are established for inference on the model parametric and nonparametric components. In addition, large number properties are presented and the finite sample behavior of the proposed estimators is evaluated through simulation studies, estimators from the proposed method perform satisfactorily on reduction of the bias. The authors apply our model to a competing risks data set from a tamoxifen trail for breast cancer study.