一类分布族的损失函数和风险函数的Bayes推断

本文考虑如下一类分布族:F(t)=[g(t)]θ,-∞A0(1)其中g(t)是关于t单调递增的可微函数,且g(A)=0,g(B)=1.在共轭先验分布下研究了未知参数η=1θ的损失函数和风险函数的B ayes估计及其保守性质,并给出相应的B ayes估计的合理性.     

Information Inequalities in a Family of Uniform Distributions

For a family of uniform distributions, it is shown that for any small < 0 the average mean squared error (MSE) of any estimator in the interval of values of length and centered at ₀ can not be smaller than that of the midrange up to the order o(n ^–2) as the size n of sample tends to infinity. The asymptotic lower bound for the average MSE is also shown to be sharp.     

绝对损失下双边截断型分布族参数的渐近最优经验Bayes估计

本文在绝对损失下构造了双边截断型分布族参数的经验Bayes估计,并在合适的条件下证明了该估计的渐近最优性.最后,给出两个有关本文主要结果的例子.     

Levy分布参数估计的损失函数和风险函数的Bayes推断

给出了在共轭先验分布下,L evy分布参数估计的损失函数和风险函数的Bayes估计及其为保守估计的一般条件,说明了该条件的合理性,并用S&P 500$close数据进行了实证分析支持我们的结论.     

正态分布在不同先验下的Bayes估计及风险比较

本文讨论在均值未知,方差已知的正态分布情况下通过在共轭先验以及Jeffreys先验二种先验下的Bayes估计问题,在平方损失函数下和线性损失函数下Bayes风险的比较.数据计算可以看出,在Jeffreys先验下的Bayes风险要比在共轭先验下的Bayes风险要大,但是当样本量增大时,两者的后验风险越来越靠近.     

连续型单参数指数族的经验Bayes检验

本文讨论了连续型单参数指数族的经验Bayes检验问题 .利用核估计方法构造了EB检验函数并获得了它的收敛速度 .     

Estimation of a common parameter for pooled samples from the uniform distributions

Summary The problem to estimate a common parameter for the pooled sample from the uniform distributions is discussed in the presence of nuisance parameters. The maximum likelihood estimator (MLE) and others are compared and it is shown that the MLE based on the pooled sample is not (asymptotically) efficient.     

Optimal Transportation-entropy Inequalities for Several Usual Distributions on R

In this paper,based on the recent results of Gozlan and Léonard we give optimal transportationentropy inequalities for several usual distributions on R,such as Bernoulli,Binomial,Poisson,Gamma distributions and infinitely divisible distributions with positive or negative jumps.     

非指数分布数族参数的经验Bayes估计的收敛速度

在“平方损失”下,研究了非指数分布族参数θ的经验Bayes估计,首先利用概率密度函数的核估计,构造了位置参数的经验Bayes（EB）估计量,在适当的条件下获得了它的收敛速度．     

绝对值损失下单边截断型分布族参数的经验Bayes估计

本文在绝对值损失下,构造了单边截断型分布族参数的EB估计,并证明了在一组条件下,其Bayes风险的收敛速度为0((ln n/n)~(λγ/(2r+))·M_n),其中0<λ,γ≤1,M_n≤ln ln n(n充分大),M_n为一无穷大量。     

The lower bound for the variance of unbiased estimators for one-directional family of distributions

Summary In this paper we introduce the concept of one-directionality which includes both cases of location (and scale) parameter and selection parameter and also other cases, and establish some theorems for shapr lower bounds and for the existence of zero variance unbiased estimator for this class of non-regular distributions.     

一种对称损失函数下一类指数分布族刻度参数的估计

在p,q对称熵损失函数L(θ,δ)=θp/δp+δq/θq-2(p,q0)下,研究了一类指数分布族c(x,n)θ-ve-T(x)/θ的刻度参数θ的Bayes估计与可容许估计,并应用积分变换定理证明了这两个估计具有不变性.     

广义Pareto分布参数的经验Bayes估计的收敛速度

在加权平方损失函数下,获得广义Pareto分布形状参数的经验Bayes(EB)估计,并得到了该估计的收敛速度.     

一维双边截断型分布族中参数函数的经验Bayes估计及其收敛速度

对一维双边截断型分布族构造了参数函数的经验 Ｂａｙｅｓ 估计,在适当的条件下给出了相应的收敛速度,并说明此收敛速度可充分接近 １２ ．     

广义双曲线分布模型在我国证券市场风险度量中的应用研究

经济的全球化、衍生产品的大量出现以及因此导致的金融市场的动荡使得金融机构越来越需要更有效的风险管理方法。而如何精确度量风险是风险管理的关键问题。本文试图从金融收益分布假设着手改善风险度量的精度。国外学者研究发现广义双曲线分布比其它分布形式可以更好地拟合实际收益分布特征。本文首次把广义双曲线分布应用到VaR的分析方法中计算我国股票指数的VaR。实证结果表明，基于广义双曲线分布的方法得到了较好的预测结果。     

对称熵损失下的一类指数族刻度参数估计

In this paper we investigate the estimator for the rth power of the scale parameter in a class of exponential family under symmetric entropy loss L（θ, δ） = v（θ/δ ＋ δ/θ - 2）. An exact form of the minimum risk equivariant estimator under symmetric entropy loss is given, and the minimaxity of the minimum risk equivariant estimator is proved. The results with regard to admissibility and inadmissibility of a class of linear estimators of the form cT（X） ＋ d are given, where T（X） Gamma（v, θ）.     

NA样本下Pareto分布参数的经验Bayes估计

讨论了Pareto分布在平方损失下参数的Bayes估计,采用同分布负相协样本的核估计方法讨论了参数的经验Bayes(EB)估计问题,并计算了给定条件下参数的经验Bayes估计的收敛速度。最后,对我国高收入阶层的财富分布情况进行了实证分析,实证分析表明我国高收入阶层的财富分布是可以用Pareto分布来描述的。     

An application of the Morgenstern family with standard two‐sided power and gamma marginal distributions to the Bayes premium in the collective risk model

The Bayes premium is a quantity of interest in the actuarial collective risk model, under which certain hypotheses are assumed. The usual assumption of independence among risk profiles is very convenient from a computational point of view but is not always realistic. Recently, several authors in the field of actuarial and operational risks have examined the incorporation of some dependence in their models. In this paper, we approach this topic by using and developing a Farlie–Gumbel–Morgenstern (FGM) family of prior distributions with specified marginals given by standard two‐sided power and gamma distributions. An alternative Poisson–Lindley distribution is also used to model the count data as the number of claims. For the model considered, closed expressions of the main quantities of interest are obtained, which permit us to investigate the behavior of the Bayes premium under the dependence structure adopted (Farlie–Gumbel–Morgenstern) when the independence case is included. Copyright © 2012 John Wiley & Sons, Ltd.     

连续型单参数指数族参数的经验Bayes估计问题:NA样本情形

对连续型单参数指数族在平方损失下导出了参数的Bayes估计,利用同分布负相协(NA)样本构造了经验Bayes(EB)估计量,并在适当条件下获得了EB估计的收敛速度.文末给出一个满足定理条件的例子.     

正态──正态结构串联系统可靠度的Bayes估计

本文利用Ｂａｙｅｓ方法讨论了正态——正态结构串联系统可靠度θ＝Ｐ_ｒ０（Ｘ＞Ｙ）的估计问题，把θ的后验均值作为它的点估计，在特殊情况下，还得到了θ的Ｂａｙｅｓ置信限。