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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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??In the additive regression models, the single-index model is considered commonly for high dimensional regression analysis. The specification of this model that it is more flexible compared with a parametric model, and it avoids the curse of dimensionality because the single-index reduces the dimensionality of a standard variable vector (x in the multi-regression) to a univariate index (\beta^\T X in the single-index model). In this paper, we developed a single-index regression model with a functional errors' term that serves in checking the heteroscedasticity. Since the efficient inference of a regression model demands that heteroscedasticity is regarded when it exists, this paper presents the assumptions of testing variance constancy in single-index models. The test statistic is assessing the variance homogeneity stated as a combination of Levene's test and the theories of ANOVA for the infinite factor levels. The test statistic in the simulation studies displays appropriately in all situations compared to a well-known method and applies to a real dataset.     

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In this paper, we study the stochastic comparisons of order statistics from generalized normal distributions. We obtain some sufficient conditions for ordering results based on parameter matrix and vector majorization comparisons. These conditions are necessary in some cases.     

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??n this paper, we propose composite quantile regression for functional linear model with dependent data, in which the errors are from a short-range dependent and strictly stationary linear process. The functional principal component analysis is employed to approximate the slope function and the functional predictive variable respectively to construct an estimator of the slope function, and the convergence rate of the estimator is obtained under some regularity conditions. Simulation studies and a real data analysis are presented for illustration of the performance of the proposed estimator.     

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In this paper, we introduce the definitions of geometric strongly ergodic, strongly ergodic and weakly ergodic for continuous-state Markov chains, then we give a primary proof of equivalence of the ergodicities for continuous-state Markov chains.     

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This paper assumes that company's asset process follows a non-linear model, which reflects the relationship between the operation costs and the size business. Suppose that the company can control the asset process by changing the size of business, paying dividends and raising money dynamically. Meanwhile, it bears both fixed and proportional transaction costs during the control processes. Under the objective of maximizing the company's value, we obtain the explicit solutions of optimal strategies and value function by using the optimal control method. The results illustrate that the optimal strategies depend on the parameters of the model. The company should expand the business scale with the increasing of asset. Dividends should be paid out according to the impulse control strategy. Financing is profitable to avoid bankruptcy if and only if the transaction costs are relatively low.     

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??In this paper, by applying the moment inequality for asymptotically almost negatively associated (AANA, in short) random sequence and truncated method, the equivalent conditions of complete moment convergence of the maximum partial for weighted sums of AANA random variables are obtained without assumptions of identical distribution, which generalize and improve the corresponding ones of{15},{16} and {17}, respectively.     

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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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??In this paper we consider a class of fractional stochastic partial differential equation driven by fractional noise. We prove that the solution admits a smooth density at any fixed point (t,x)in[0,T]timesmathbb{R} with T>0 by using the techniques of Malliavin calculus.     

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多元非参数分位数回归常常是难于估计的, 为了降低维数同时保持非参数估计的灵活性, 人们常常用单指标的方法模拟响应变量的条件分位数. 本文主要研究单指标分位数回归的变量选择. 以最小化平均损失估计为基础, 我们通过最小化具有SCAD惩罚项的平均损失进行变量选择和参数估计. 在正则条件下, 得到了单指标分位数回归SCAD变量选择的Oracle性质, 给出了SCAD变量选择的计算方法, 并通过模拟研究说明了本文所提方法变量选择的样本性质.     

Analysis of the M/M/1 Queue with Processor Sharing via Spectral Theory

We show in this paper that the computation of the distribution of the sojourn time of an arbitrary customer in a M/M/1 with the processor sharing discipline (abbreviated to M/M/1 PS queue) can be formulated as a spectral problem for a self-adjoint operator. This approach allows us to improve the existing results for this queue in two directions. First, the orthogonal structure underlying the M/M/1 PS queue is revealed. Second, an integral representation of the distribution of the sojourn time of a customer entering the system while there are n customers in service is obtained.     

多源验前信息之下Bayes可靠性估计

本文考虑存在多源验前信息的情况，以二项分布为例，首先把各种验前信息化成不同的约束条件，并运用最大熵准则推导出各种验前信息所对应的验前分布，然后将这些分布综合成最终的验前分布，最后根据系统的寿命试验数据得出可靠性参数的验后分布并进行了Ｂａｙｅｓ推断，文中给出了仿真实例以说明方法的有效性。     

Bayes分析中多源验前信息融合的ML-II方法

在Bayes小子样理论中,验前分布的获取和表示是一个关键问题.针对工程实践中遇到的验前信息的多源性,给出了一种基于第二类极大似然估计原理(M L-II)的多源异总体验前分布的融合方法,并通过仿真实例证明了该方法的有效性.     

关于最大熵与信息熵之差的上界讨论

基于自信息函数为一可微凸函数这一事实,利用自信息函数所对应的Jenson离散型不等式,得到了有关最大熵与信息熵之差上界的一些结果.