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The heteroscedasticity is inevitable for the panel data modeling in economics. The two-stage estimation method is a better means to study the heteroscedasticity, in which the basis is to select only one independent variable for samples grouping, it can cause the information used is incomplete. In this paper, we propose to select several variables for grouping using variable selection method, then k-mean algorithm is used to cluster, so the samples classification can be achieved and the heteroscedasticity estimation can be obtained. The results of real example analysis show that the method presented in this paper has obvious advantages in effectiveness and feasibility.     

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??How to solve the inference problem of candidate database web surveys is an urgent problem to be solved in the development of web survey. In order to solve this problem, the inference method of non-probability sampling based on superpopulation pseudo design and the combined sample is proposed. A superpopulation model is firstly built up to construct pseudo weights for a survey sample of the web candidate database. The estimator of the population mean is then computed according to the combined sample composed of the survey sample of the web candidate database and a probability sample. The variance estimator of the population mean estimator is lastly derived according to the variance estimation theory of the superpopulation model. The Bootstrap and Jackknife methods are also used to compute the variance estimator. And all these variance estimation methods are compared. The research results show that the population mean estimator based on superpopulation pseudo design and the combined sample is better, and has higher efficiency than the estimator only using the probability sample and the weighted estimator only using the survey sample of the web candidate database. The variance estimator computed by using the VM1, VM2 and VM3 method are relatively better.     

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In this paper, we establish the option pricing model under sub-fractional Brownian motion, and consider the situation of the continuous dividend payments. Firstly, Wick-It^{o} integral and partial differential method are used to get the option price of partial differential equation, and then through variable substitution into Cauchy problem, we can get the pricing formula of European call option with dividend-paying in sub-fractional Brownian motion environment.According to the pricing formula of European call option, the European put option pricing formula is obtained. Moreover, we study the parameter estimation in the model, and consider the unbiasedness and the strong convergence of the estimator.     

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本文主要讨论了变点的先验分布为beta-binomial分布 和Ibrahim等(2003)提出的幂型先验的条件下, 有一个变点的线性模型的贝叶斯统计推断问题, 并且我们假定变点两边的观测值的方差是相等的. 我们得到变点、回归系数、共同方差的后要分布的显示表达式. 本论文不仅把Ferrira(1975)论文从变点先验分布服从离散均匀分布推广到了更好描述变点 的形状的beta-binomial分布, 而且进一步将变点的先验分布推广到包含的历史信息的幂型先验. 当变点的先验分布为beta-binomial分布和幂型先验时, 模拟结果显示了贝叶斯方法具有更高的准确性.     

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Let p_M(t,x,y) be the minimal heat kernel of a d-dimenional compact Riemannian manifold M for any time t\in(0,1] and x,y\in M. Using the horizontal Brown bridge on M, we prove that, for any nonnegative integers n and m, there is a constant C depending on n,m and the manifold M, such that |\nabla^n_x\nabla^m_y\ln p_M(t,x,y)|\leq C[d(x,y)/t+1/\sqrt{t}\,]^{n+m}$, which generalizes the conclusion of the higher derivatives of the logarithmic heat kernel \ln p_M(t,x,y) about single variable in \ncite{1}.     

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??The Bayesian model are established for the VaR and related risk measurements. The relationship between VaR and other risk measurements including expect shortfall, tail condition expectation and conditional value at risk are discussed. Furthermore, the Bayesian estimates and Bayesian predictors of these risk measurement are derived. Thirdly, the consistency and asymptotic normality in the exponential risk model are proved. Finally, the numerical simulation method is used to verify the convergence rate under different sample sizes.     

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This paper considers the asymptotics of randomly weighted sums and their maxima, where the increments {X_i,i\geq1\} is a sequence of independent, identically distributed and real-valued random variables and the weights {\theta_i,i\geq1\} form another sequence of non-negative and independent random variables, and the two sequences of random variables follow some dependence structures. When the common distribution F of the increments belongs to dominant variation class, we obtain some weakly asymptotic estimations for the tail probability of randomly weighted sums and their maxima. In particular, when the F belongs to consistent variation class, some asymptotic formulas is presented. Finally, these results are applied to the asymptotic estimation for the ruin probability.     

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In this paper, we establish a local representation theorem for generators of reflected backward stochastic differential equations (RBSDEs), whose generators are continuous with linear growth. It generalizes some known representation theorems for generators of backward stochastic differential equations (BSDEs). As some applications, a general converse comparison theorem for RBSDEs is obtained and some properties of RBSDEs are discussed.     

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This paper studies the estimation of change point in mean and variance function of a non-parametric regression model based on kernel estimation and wavelet method. First, kernel estimation of mean function is developed and it is used to estimate the position and jump size of mean change. Second, wavelet methods are applied to derive the variance estimator which is used to estimate the location and jump size of the change point in variance. The asymptotic properties of these estimators are proved. Finally, the results from a numerical simulations and comparison study show that validate the effectiveness of our method.     

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VaR风险度量在金融、保险中有重要的应用. 本文建立了贝叶斯模型, 在某种损失函数下研究了VaR风险度量的贝叶斯估计. 证明了指数-伽马分布下贝叶斯估计的强相合性和渐近正态性, 最后利用数值模拟的方法验证了不同样本容量下估计的收敛速度.     

Linear Minimax Prediction in a Finite Population with Ellipsoidal Constraints

Under a matrix loss function, we investigate the prediction problem in a finite population with ellipsoidal restriction in this paper. Firstly, a class of homogeneous linear minimax predictors for finite population regression coefficient are obtained. Moreover, it is shown that the linear minimax predictors are admissible in the class of homogeneous linear predictors. Finally, a simulation study and a real data example are used to illustrate our results.     

二次损失下线性预测的可容许性

本文在二次损失下研究了任意秩有限总体中线性预测的可容性，得到了线性预测Lys(Lys a)是可容许线性预测的充要条件．     

矩阵损失下线性预测的可容许性

在矩阵损失下研究了任意秩有限总体中线性预测的可容许性,得到了线性预测Lys(Lys α) 是可容许线性预测的充要条件.     

矩阵损失下一般Gauss-Markov模型中回归系数的线性MINIMAX估计

设Y是具有均值Xβ和协方差阵σ2V的n维随机向量，Sβ是线性可估函数，这里X，S和V0是已知矩阵，β∈Rp和σ2＞0是未知参数．本文在矩阵损失下研究了线性估计的Minimax性．在适当的假设下，得到了Sβ的唯一线性Minimax估计（有关唯一性在几乎处处意义下理解）．     

多元线性模型中回归系数的线性可容许估计

基于Zellner的平衡损失的思想,本文提出了矩阵形式的平衡损失函数,并在该损失函数下讨论了多元回归系数线性估计的可容许性.给出了六种不同形式的可容许定义,证明了这六种容许性在齐次和非齐次线性估计类中是一致的,且得到了其共同的可容许估计的充要条件.     

带有非中心不完全椭球约束的线性模型中线性估计的可容许性

本文研究了线性模型(Y,Xβ,σ2V V≥0)在非中心不完全椭球约束:(β-β0)’N(β-β0)≤σ2,N≥0下椭球中心β0对线性估计的可容许性的影响,证明了对于具有某种结构的β1和β2,线性模型(Y,Xβ,σ2V,V≥0)在非中心不完全椭球约束:(β-β1)’N(β-β1)≤σ2,N≥0与非中心不完全椭球约束:(β-β2)’N(β-β2)≤σ2,N≥0下的可容许线性估计类是相同的．     

带有不完全椭球约束的线性模型中线性估计的可容许性

本文刻划了线性模型（Ｙ，Ｘβ，σ２Ｖ，Ｖ≥０）在不完全椭球约束：（β－β０）’Ｎ（β－ β Ｐ０）≤σ２，Ｎ ≥ ０下的线性估计的可容许性．本文的结果显示了一个有趣的现象，即一个线性估计在全体线性估计所组成的类中的可容许性与椭球的中心β０无关，而在全体齐次线性估计所组成的类中的可容许性与β０有关．     

平衡损失下一般Gauss—Markoff模型中回归系数的非齐次线性可容许估计

提出了适用于—般Gauss-Markoff模型的平衡损失函数,并在该平衡损失下,研究了模型中回归系数的非齐次线性估计在非齐次线性估计类中的可容许性,得到了充要条件．     

矩阵损失下随机回归系数和参数的线性Minimax估计

对于一般的随机效应线性模型Y=Xβ+ε,这里β和ε分别是p维和n维的随机向量,且E(βε)=(Aa0),Cov(βε)=σ2(V10 0V2),(Vi≥0,i=1,2)我们定义了Sα+Qβ的线性Minimax估计,在一定条件下得到了Sα+Qβ在线性估计类中的Minimax估计,并在几乎处处意义下证明了它的唯一性.     

平衡损失下有限总体回归系数的线性可容许预测

本文研究了平衡损失函数下正态总体和非正态总体中有限回归系数的可容许预测.利用统计决策理论,获得了非正态总体中齐次线性预测为可容许预测的充分必要条件和在正态总体中齐次线性预测在一切预测类中可容许性的充要条件,推广了二次损失下的若干相关结果.