Estimating a model through the conditional MLE

The estimation problem of a model through the conditional maximum likelihood estimator (MLE) is explored. The estimated model is compared using the two dual Kullback-Leibler losses with that through the unconditional MLE. The former is found to be superior to the latter under familiar models. This result is applicable to the model selection problem. These suggest a novel extensive use of the conditional likelihood, since the traditional use of the conditional likelihood was restricted only on inference for the structural parameter.     

The Kullback-Leibler risk of the Stein estimator and the conditional MLE

The decomposition of the Kullback-Leibler risk of the maximum likelihood estimator (MLE) is discussed in relation to the Stein estimator and the conditional MLE. A notable correspondence between the decomposition in terms of the Stein estimator and that in terms of the conditional MLE is observed. This decomposition reflects that of the expected log-likelihood ratio. Accordingly, it is concluded that these modified estimators reduce the risk by reducing the expected log-likelihood ratio. The empirical Bayes method is discussed from this point of view.     

Towards a unification of certain characterizations by conditional expectations

The paper presents a characterization of a general family of distributions by the form of the expectation of an appropriately truncated function of the random variable involved. The obtained result unifies results existing in the literature for specific distributions as well as new results that appear for the first time in this paper. A discrete version is also provided unifying existing characterizations of known discrete distributions.     

独立Poisson分布的均值之MLE的改进

In this paper, we consider the simultaneous estimation of the parameters (means) of the independent Poisson distribution by using the following loss functions: L0(θ,T)=∑i=1^n(Ti-θi)^2,L1(θ,T)=∑i=1^n(Ti-θi)^2/θi We develop an estimator which is better than the maximum likelihood estimator X simultaneously under L0(θ, T) and L1(θ, T). Our estimator possesses substantially smaller risk than the usual estimator X to estimate the parameters (means) of the independent Poisson distribution.     

Characterizations of the Poisson process as a renewal process via two conditional moments

Given two independent positive random variables, under some minor conditions, it is known that fromE(X^rX+Y)=a(X+Y)^r andE(X^sX+Y)=b(X+Y)^s, for certain pairs ofr ands, wherea andb are two constants, we can characterizeX andY to have gamma distributions. Inspired by this, in this article we will characterize the Poisson process among the class of renewal processes via two conditional moments. More precisely, let {A(t), t0} be a renewal process, with {S _k, k1} the sequence of arrival times, andF the common distribution function of the inter-arrival times. We prove that for some fixedn andk, kn, ifE(S _k ^r A(t)=n)=at^r andE(S _k ^s A(t)=n)=bt^s, for certain pairs ofr ands, wherea andb are independent oft, then {A(t), t0} has to be a Poisson process. We also give some corresponding results about characterizingFto be geometric whenF is discrete.Support for this research was provided in part by the National Science Council of the Republic of China, Grant No. NSC 81-0208-M110-06.     

CONSISTENCY OF MLE OF THE PARAMETER OF EXPONENTIAL LIFETIME DISTRIBUTION FOR RANDOM CENSORING MODEL WITH INCOMPLETE INFORMATION

In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator (MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.     

Computing the variance of a conditional expectation via non-nested Monte Carlo

Computing the variance of a conditional expectation has often been of importance in uncertainty quantification. Sun et al. has introduced an unbiased nested Monte Carlo estimator, which they call $1\frac{1}{2}$-level simulation since the optimal inner-level sample size is bounded as the computational budget increases. In this letter, we construct unbiased non-nested Monte Carlo estimators based on the so-called pick-freeze scheme due to Sobol’. An extension of our approach to compute higher order moments of a conditional expectation is also discussed.     

保险损失费分布研究

对保险公司关注的保险总损失费的分布和平均总损失费的置信上限进行了初步研究.基于危险事故的保险损失费为服从指数分布的随机变量,在投保人数为泊松随机变量的条件下,根据各投保个体损失费分布参数的不同情况,导出某一时间内总损失费的分布密度和均值.在投保人数确定的条件下,研究了给定置信度下平均总损失费的置信上限,并给出了数字例.     

Constructing elementary procedures for inference of the gamma distribution

The aim of the present paper is to construct a series of estimators and tests in the one and the two sample problems in the gamma distribution through the Kullback-Leibler loss. Some of them are newly introduced here. When the approach is applied to the case of the normal distribution, the well known estimators and tests are derived. It is found that the conditional maximum likelihood estimator of the dispersion parameter plays a key role.     

������������˫����ָ���ֲ���Ʒƽ���������ʵ�ͳ���ƶ�

本文利用广义p值和广义置信区间理论,研究了两独立服从双参数指数分布产品平均寿命比率的统计推断问题.给出了平均寿命比率的广义置信区间,并对该区间的覆盖率和区间长度进行了数据模拟,模拟结果与已有文献中的近似置信区间进行了比较,结果显示本文给出的广义置信区间的区间覆盖率和区间长度都要优于近似置信区间,特别是在小样本的情况下.     

Decision Theoretic Estimation of the Ratio of Variances in a Bivariate Normal Distribution

In this paper the problem of estimating the ratio of variances, , in a bivariate normal distribution with unknown mean is considered from a decision-theoretic point of view. First, the UMVU estimator of is derived, and then it is shown to be inadmissible under two specific loss functions, namely, the squared error loss and the entropy loss. The derivation of the results is done by conditioning on an auxiliary negative binomial random variable.     

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.     

Estimation of the ratio of the scale parameters of two exponential distributions with unknown location parameters

We consider the estimation of the ratio of the scale parameters of two independent two-parameter exponential distributions with unknown location parameters. It is shown that the best affine equivariant estimator (BAEE) is inadmissible under any loss function from a large class of bowl-shaped loss functions. Two new classes of improved estimators are obtained. Some values of the risk functions of the BAEE and two improved estimators are evaluated for two particular loss functions. Our results are parallel to those of Zidek (1973, Ann. Statist., 1, 264–278), who derived a class of estimators that dominate the BAEE of the scale parameter of a two-parameter exponential distribution.     

风险非同质时索赔次数的分布拟合及其EM算法

本文运用EM算法,对于风险非同质时索赔次数的分布,分别给出了离散型多元风险模型,混合两伽玛模型参数的极大似然估计的迭代公式,并将其应用到一个实际问题中去,效果较好。     

第二讲:成败型情形和指数分布情形的可靠性评定

对于成败型情形,基于成功次数给出了成功率的优良置信限和置信区间;对于产品寿命服从指数分布的情形,针对不同类型的数据(定数截尾、定时截尾、定总时与定数混合截尾、工型区间删失等)分别给出了可靠性参数(平均无故障时间(MTBF),可靠度,可靠寿命)的点估计和置信限。     

均值矩阵的函数的所有可容许估计

对于多元正态线性模型Ｙｎｘｍ～Ｎ（Ｘθ,σ２∑Ｖ）,在四种不同的可容许意义下,本文研究了ＳＸθ的线性估计ＬＹ＋Ｄ在一切估计类中的可容许性在适当条件下得到了充要条件,在一般情况给出了充分条件和必要条件．     

双参数指数分布环境因子的Bayes估计

讨论了定数截尾样本下双参数指数分布环境因子的极大似然估计、区间估计和Bayes估计.以参数后验密度的商密度作为环境因子的后验密度,并结合专家经验运用Bayes方法给出了环境因子在平方损失下和LINEX损失下的Bayes估计.最后运用Monte Carlo方法对各估计结果的均方误差(MSE),进行了模拟比较.结果表明LINEX损失下环境因子的估计较好.     

Some Properties and Improvements of the Saddlepoint Approximation in Nonlinear Regression

We summarize properties of the saddlepoint approximation of the density of the maximum likelihood estimator in nonlinear regression with normal errors: accuracy, range of validity, equivariance. We give a geometric insight into the accuracy of the saddlepoint density for finite samples. The role of the Riemannian curvature tensor in the whole investigation of the properties is demonstrated. By adding terms containing this tensor we improve the saddlepoint approximation. When this tensor is zero, or when the number of observations is large, we have pivotal, independent, and ² distributed variables, like in a linear model. Consequences for experimental design or for constructions of confidence regions are discussed.