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Variance related premium principle is one of the most important principles not only in practice applications but also in research field of actuarial science. In this paper, the Bayesian models are established under variance related premium principle. The Bayesian estimate and credibility estimate of risk premium are derived. Furthermore, some statistical properties of estimators are discussed. In the models with multitude contract data, the unbiased consistent estimates of the structure parameters are proposed. Finally, the empirical Bayes estimator are proved to be asymptotically optimal.     

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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 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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In this article, using the limit theory of martingales, we study the moderate deviation for maximum likelihood estimator of unknown parameter in the stochastic partial differential equation driven by additive fractional Brownian motion with Hurst parameter, and the rate function can be calculated. Moreover, we apply our main result to several examples.     

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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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This paper concerns with the estimation of a fixed effects panel data partially linear regression model with the idiosyncratic errors being an autoregressive process. For fixed effects short time series panel data, the commonly used autoregressive error structure fitting method will not result in a consistent estimator of the autoregressive coefficients. Here we propose an alternative estimation and show that the resulting estimator of the autoregressive coefficients is consistent and this method is workable for any order autoregressive error structure. Moreover, combining the B-spline approximation, profile least squares dummy variable (PLSDV) technique and consistently estimated the autoregressive error structure, we develop a weighted PLSDV estimator for the parametric component and a weighted B-spline series (BS) estimator for the nonparametric component. The weighted PLSDV estimator is shown to be asymptotically normal and more asymptotically efficient than the one which ignores the error autoregressive structure. In addition, this paper derives the asymptotic bias of the weighted BS estimator and establish its asymptotic normality as well. Simulation studies and an example of application are conducted to illustrate the finite sample performance of the proposed procedures.     

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本文给出了上期望空间中独立随机变量部分和的最大不等式、指数 不等式、Marcinkiewicz-Zygmund不等式. 并且应用指数不等式和Marcinkiewicz-Zygmund不等式 研究了随机变量部分和序列完备收敛的性质.     

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??In this paper we describe the excursions from a set explicitly for
recurrent Markov chain with discrete time. A new exit system is presented through using a
law conditioned by specifying the starting point and ending point of excursions. In a simple
case, we verify that our conditioned excursion law is a discrete approximation for that of
a diffusion.     

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Let,,,
be all independent PRHR variables. Firstly, we show thatimplies. Secondly, we consider the comparison of
convolutions of independent heterogeneous PRHR variables with respect to the usual stochastic
ordering. Suppose and, we prove that implies,
for all. The results established here strengthen some of the results known in
the literature.     

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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.     

A Localized Implementation of the Iterative Proportional Scaling Procedure for Gaussian Graphical Models

In this article, we propose localized implementations of the iterative proportional scaling (IPS) procedure by the strategy of partitioning cliques for computing maximum likelihood estimations in large Gaussian graphical models. We first divide the set of cliques into several nonoverlapping and nonempty blocks, and then adjust clique marginals in each block locally. Thus, high-order matrix operations can be avoided and the IPS procedure is accelerated. We modify the Swendsen–Wang Algorithm and apply the simulated annealing algorithm to find an approximation to the optimal partition which leads to the least complexity. This strategy of partitioning cliques can also speed up the existing IIPS and IHT procedures. Numerical experiments are presented to demonstrate the competitive performance of our new implementations and strategies.     

A Class of Strong Deviation Theorems for the Random Fields Associated with Nonhomogeneous Markov Chains Indexed by a Bethe Tree

In this article, we establish a class of strong deviation theorems for the random fields which are associated with nonhomogeneous Markov chains indexed by a Bethe tree. As corollaries, we obtain the strong law of large numbers and asymptotic equipartition property for nonhomogeneous Markov chains indexed by such tree.     

Cayley树上非对称马氏链的强大数定律及渐近均分割性

In this paper,we study the strong law of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain（NSMC） indexed by Cayley tree with any finite states.The asymptotic equipartition properties with almost everywhere（a.e.） convergence for NSMC indexed by Cayley tree are obtained.This article generalizes a recent result.