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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.     

State-space stochastic volatility models: A review of estimation algorithms

Stochastic volatility models (SVMs) represent an important framework for the analysis of financial time series data, together with ARCH-type models; but unlike the latter, the former, at least from the statistical point of view, cannot rely on the possibility of obtaining exact inference, in particular with regard to maximum likelihood estimates for the parameters of interest. For SVMs, usually only approximate results can be obtained, unless particularly sophisticated estimation strategies like exact non-gaussian filtering methods or simulation techniques are employed. In this paper we review SVM and present a new characterization for them, called ‘generalized bilinear stochastic volatility’. © 1996 John Wiley & Sons, Ltd.     

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本文综述混合效应模型参数估计方面的若干新进展. 平衡混合效应方差分析模型的协方差阵具有一定结构. 对这类模型, 文献[1]提出了参数估计的一种新方法, 称为谱分解法. 新方法的突出特点是, 能同时给出固定效应和方差分量的估计, 前者是线性的, 后者是二次的,且相互独立. 而后, 文献[2--9]证明了谱分解估计的进一步的统计性质, 同时给出了协方差阵对应的估计, 它不仅是正定阵, 而且可获得它的风险函数, 这些文献还研究了谱分解估计与方差分析估计, 极大似然估计, 限制极大似然估计以及最小范数二次无偏估计的关系. 本文综述这一方向的部分研究成果, 并提出一些待进一步研究的问题.     

On the parametrization of autoregressive models by partial autocorrelations

One of the difficulties that arise in the statistical analysis of autoregressive schemes is the very complex nature of the domain of the regression parameters. In the present paper we study an alternative parametrization of autoregressive models of finite order, namely the parametrization by the partial autocorrelations. These are shown to vary freely from −1 to +1 and to be in a one-to-one, continuously differentiable correspondence with the regression parameters. Properties of the asymptotic normal distribution of the maximum likelihood estimates are discussed, and we present a new deduction of Quenouille's result on the asymptotic independence of some of the estimated partial autocorrelations.     

On statistical models for regression diagnostics

In regression diagnostics, the case deletion model (CDM) and the mean shift outlier model (MSOM) are commonly used in practice. In this paper we show that the estimates of CDM and MSOM are equal in a wide class of statistical models, which include LSE, MLE, Bayesian estimate andM-estimate in linear and nonlinear regression models; MLE in generalized linear models and exponential family nonlinear models; MLEs of transformation parameters of explanatory variables in a Box-Cox regression models and so on. Furthermore, we study some models, in which, the estimates are not exactly equal but are approximately equal for CDM and MSOM.     

Linear mixed models and penalized least squares

Linear mixed-effects models are an important class of statistical models that are used directly in many fields of applications and also are used as iterative steps in fitting other types of mixed-effects models, such as generalized linear mixed models. The parameters in these models are typically estimated by maximum likelihood or restricted maximum likelihood. In general, there is no closed-form solution for these estimates and they must be determined by iterative algorithms such as EM iterations or general nonlinear optimization. Many of the intermediate calculations for such iterations have been expressed as generalized least squares problems. We show that an alternative representation as a penalized least squares problem has many advantageous computational properties including the ability to evaluate explicitly a profiled log-likelihood or log-restricted likelihood, the gradient and Hessian of this profiled objective, and an ECME update to refine this objective.     

Variable selection for fixed effects varying coefficient models

We consider the problem of variable selection for the fixed effects varying coefficient models.A variable selection procedure is developed using basis function approximations and group nonconcave penalized functions, and the fixed effects are removed using the proper weight matrices. The proposed procedure simultaneously removes the fixed individual effects, selects the significant variables and estimates the nonzero coefficient functions. With appropriate selection of the tuning parameters, an asymptotic theory for the resulting estimates is established under suitable conditions. Simulation studies are carried out to assess the performance of our proposed method, and a real data set is analyzed for further illustration.     

方差分量的广义谱分解估计

对于随机效应部分为一般平衡多向分类的线性混合模型,将王松桂(2002)提出的一种称之为谱分解估计的参数估计新方法推广到随机效应设计阵为任意矩阵的含两个方差分量的线性混合模型,给出了方差分量的广义谱分解估计方法,并证明了所得估计的一些统计性质。另外,还就广义谱分解估计类中某些特殊估计和对应的方差分析估计进行了比较,得到了它们相等的充分必要条件。     

A statistical approach to graduation by mathematical formula

Graduation by mathematical formula is recast as problem of statistical estimation. The method of maximum likelihood is used to determine the estimates of the parameters. Theory is developed to allow for estimation without resorting to the usual ‘exposure’ formulas. Both single and multiple decrement models are considered. Theoretical results are obtained for some specific mortality models. Numerical procedures to obtain the estimates are considered.     

混合系数线性模型参数的Stein估计

在连续测量数据情况下,对混合系数线性模型给出了固定系数和随机系数的两种形式的Ｓｔｅｉｎ估计,并证明了在均方误差意义下,Ｓｔｅｉｎ估计要优于ＬＳ估计,最后还讨论了Ｓｔｅｉｎ压缩系数的选取方法     

基于经验似然的部分线性模型的统计诊断

经验似然方法己经被广泛应用于许多模型的统计推断.本文基于经验似然对部分线性模型进行统计诊断.首先给出模型的估计方程,进而得到模型参数的极大经验似然估计;其次,基于经验似然研究了三种不同的影响曲率;最后通过随机模拟和实例分析,说明了统计诊断方法的有效性.     

齐次线性约束回归模型参数的主成分压缩估计

当设计矩阵X复共线时,对齐次线性约束回归模型参数的约束最小二乘估计进行改进,提出参数的主成分压缩估计,并对新参数估计的性质进行了讨论,最后进行了数值模拟,验证了算法的参数估计优于约束最小二乘估计.     

Characterizing the elements of Earth's radiative budget: Applying uncertainty quantification to the CESM

Understanding and characterizing sources of uncertainty in climate modeling is an important task. Because of the ever increasing sophistication and resolution of climate modeling it is increasingly important to develop uncertainty quantification methods that minimize the computational cost that occurs when these methods are added to climate modeling. This research explores the application of sparse stochastic collocation with polynomial edge detection to characterize portions of the probability space associated with the Earth's radiative budget in the Community Earth System Model (CESM). Specifically, we develop surrogate models with error estimates for a range of acceptable input parameters that predict statistical values of the Earth's radiative budget as derived from the CESM simulation. We extend these results in resolution from T31 to T42 and in parameter space increasing the degrees of freedom from two to three.     

基于固定效应的纵向数据分位点回归模型的参数估计及CDM和MSOM的等价性

研究了基于固定效应的纵向数据模分位点回归模型的参数估计及统计诊断问题.首先给出了参数估计的MM迭代算法,然后讨论了统计诊断中数据删除模型(CDM)和均值移模型(MSOM)的等价性问题,最后利用消炎镇痛药数据说明了方法的应用.     

Heteroscedastic Laplace mixture of experts regression models and applications

Mixture of Experts(MoE) regression models are widely studied in statistics and machine learning for modeling heterogeneity in data for regression, clustering and classification.Laplace distribution is one of the most important statistical tools to analyze thick and tail data. Laplace Mixture of Linear Experts(LMoLE) regression models are based on the Laplace distribution which is more robust. Similar to modelling variance parameter in a homogeneous population, we propose and study a new novel class of models: heteroscedastic Laplace mixture of experts regression models to analyze the heteroscedastic data coming from a heterogeneous population in this paper. The issues of maximum likelihood estimation are addressed. In particular, Minorization-Maximization(MM) algorithm for estimating the regression parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo simulations. Results from the analysis of two real data sets are presented.     

Robust-efficient credibility models with heavy-tailed claims: A mixed linear models perspective

In actuarial practice, regression models serve as a popular statistical tool for analyzing insurance data and tariff ratemaking. In this paper, we consider classical credibility models that can be embedded within the framework of mixed linear models. For inference about fixed effects and variance components, likelihood-based methods such as (restricted) maximum likelihood estimators are commonly pursued. However, it is well-known that these standard and fully efficient estimators are extremely sensitive to small deviations from hypothesized normality of random components as well as to the occurrence of outliers. To obtain better estimators for premium calculation and prediction of future claims, various robust methods have been successfully adapted to credibility theory in the actuarial literature. The objective of this work is to develop robust and efficient methods for credibility when heavy-tailed claims are approximately log-location-scale distributed. To accomplish that, we first show how to express additive credibility models such as Bühlmann-Straub and Hachemeister ones as mixed linear models with symmetric or asymmetric errors. Then, we adjust adaptively truncated likelihood methods and compute highly robust credibility estimates for the ordinary but heavy-tailed claims part. Finally, we treat the identified excess claims separately and find robust-efficient credibility premiums. Practical performance of this approach is examined-via simulations-under several contaminating scenarios. A widely studied real-data set from workers’ compensation insurance is used to illustrate functional capabilities of the new robust credibility estimators.     

Sequential fixed accuracy estimation for nonstationary autoregressive processes

For an autoregressive process of order p, the paper proposes new sequential estimates for the unknown parameters based on the least squares (LS) method. The sequential estimates use p stopping rules for collecting the data and presumes a special modification the sample Fisher information matrix in the LS estimates. In case of Gaussian disturbances, the proposed estimates have non-asymptotic normal joint distribution for any values of unknown autoregressive parameters. It is shown that in the i.i.d. case with unspecified error distributions, the new estimates have the property of uniform asymptotic normality for unstable autoregressive processes under some general condition on the parameters. Examples of unstable autoregressive models satisfying this condition are considered.

     

Variance reduction method based on sensitivity derivatives,Part 2

A previous paper introduced a sampling method (SDES) based on sensitivity derivatives to construct statistical moment estimates that are more efficient than standard Monte Carlo estimates. In this paper we sharpen previous theoretical results and introduce a criterion to guarantee that the variance of SDES estimates is smaller than the variance of the Monte Carlo estimate. Previous numerical experiments demonstrated, and here we prove analytically, that the first-order SDES and Monte Carlo estimates converge at the same rate. We illustrate the efficiency of the SDES method of order n, where n is fixed, to estimate statistical moments with a Korteweg–de Vries equation with uncertain initial conditions.     

逐步增加Ⅱ型截尾下Pareto分布的Bayes估计

基于逐步增加的Ⅱ型截尾样本,当Pareto分布的尺度参数已知时,分别在平方损失和LINEX损失下讨论了其形状参数和可靠性指标(失效率和可靠度)的Bayes估计,并用Monte-Carlo方法对估计结果的MSE,进行了模拟比较.结果表明了在LINEX损失下的估计结果更有效.     

Analysis and finite element simulations of a second‐order fluid model in a bounded domain

This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second‐order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. The method is applied to the two‐dimensional lid‐driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic parameters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007