具有共同尺度参数的多总体指数分布的参数估计

本文讨论了具有共同尺度参数的多总体指数分布的参数估计问题；证明了尺度参数及位置参数估计的最佳仿射同变估计是不容许的，且给出相应的改进估计．     

对稳健回归尺度参数估计的一种改进

常对线性回归模型的稳健 M估计中 ,尺度参数使用绝对离差中位数 MAD.将 Rousseeuw等人对单变量尺度参数的一种稳健估计 Sn引入到回归问题中 ,讨论了此估计的一些优良性质 ,并通过一个小规模的模拟研究 ,说明使用 Sn比使用 MAD做尺度参数将会较大地提高回归估计的估计效率 .     

位置参数受约束时指数分布在定数截尾样本下的参数估计

本文考虑指数分布在定数截尾样本情况下位置多数有上界约束时，位置多数和尺度参数的估计．分别给出了有约束位置参数和尺度参数的最佳仿射同变估计在均方误基原则下的改进估计，同时研究了在Pitman准则下这些估计的比较，观察到了与均方误差原则不一致，甚至矛盾的结论．最后应用到位置参数有顺序的两个截尾指数分布，同样获得类同结果．     

Pitman准则下指数分布的参数估计

本文讨论了Ｐｉｔｍａｎ准则下指数分布的参数估计问题，证明了尺度参数与位置参数的最接近仿射同变估计是ＰＣ－不容许的，并分别给出了各自的改进估计．     

指数分布尺度参数的区间估计

本文在截尾样本情况下，讨论了指数分布尺度参数的区间估计及其改进     

Pareto分布形状参数的E-Bayes估计和多层Bayes估计及其应用

给出了参数的E-Bayes估计的定义,对Pareto分布在尺度参数已知时,在平方损失下给出了形状参数的E-Bayes估计和多层Bayes估计,并且用Monte Carlo方法给出了模拟算例.最后,结合高尔夫球手收入数据的实际问题进行了计算,结果表明本文提出的方法可行且便于应用.     

Weibull分布尺度参数的收缩估计

讨论了Ｗｅｉｂｕｌｌ分面尺度参数的收缩估计。在两种不同的参数先验信息场合，给出了不同的收缩估计。对以检验统计量函数形式给出的收缩系数进行了讨论，并用Ｍｉｏｎｔｅ－Ｃａｒｌｏ模拟方法研究了收缩估计的相对效。     

威布尔分布的Bayes可靠性分析

本文针对两参数的威布尔分布的元件，采用Ｂａｙｅｓ方法对其可靠性进行分析，文中分别对两种假设情况进行了讨论，第一种情况是形状参数为离散取值，尺度参数为连续取值的情况，第二种情况假设形状参数的先验分布为均匀分布，尺度参数的先验分布为逆伽玛分布，推出了对应的可靠性估计和置信下限估计，并给出了计算算法，最后用实例对算法进行了验证。     

MLinex损失函数下Gamma分布的尺度参数的Bayes估计

在MLinex损失函数下,利用Bayes估计方法研究了Gamma分布的尺度参数的Bayes估计,并证明了其容许性.结果是:在Mlinex损失函数下得到了Gamma分布尺度参数唯一的Bayes估计的一般表达式及其精确表达式,并证明是可容许的.最后通过数值分析实例,说明了所用的参数估计方法是合理可行的.     

加权平方和损失下线性估计的可容许性

1980年,Berger讨论了Γ分布尺度参数的通常估计的容许性向题.本文在此基础上讨论Γ分布尺度参数的线性估计的容许性问题,即 例1 设X_1和X_2相互独立,X_1～Γ(α_1,β_1~(-1)),X_2～Γ(α_2,β_2~(-1))α_1和α_2是已知的正常数,β=(β_1,β_2)′∈R~ ×R~ 是未知的参数.取β的估计为线性估计     

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.     

Classes of improved estimators for parameters of a Pareto distribution

The problem of estimating parameters of a Pareto distribution is investigated under a general scale invariant loss function when the scale parameter is restricted to the interval (0, 1]. We consider the estimation of shape parameter when the scale parameter is unknown. Techniques for improving equivariant estimators developed by Stein, Brewster–Zidek and Kubokawa are applied to derive improved estimators. In particular improved classes of estimators are obtained for the entropy loss and a symmetric loss. Risk functions of various estimators are compared numerically using simulations. It is also shown that the technique of Kubokawa produces improved estimators for estimating the scale parameter when the shape parameter is known.     

Estimators of scale parameters in linear regression

This note discusses the asymptotic distribution of two scale and location invariant estimators of two scale parameters in the multiple linear regression model. Both of these estimators need an initial estimator of the regression parameter vector. The asymptotic distribution of one of these estimators does not depend on this initial estimator. Both of these estimators are useful in the computation of scale and translation invariant adaptive estimators and M-estimators of the regression parameter vector.     

Statistical Inference for the Location and Scale Parameters of the Skew Normal Distribution

In this paper, we consider the problem of estimating the location and scale parameters of the skew normal distribution introduced by Azzalini. For this distribution, the classic maximum likelihood estimators(MLEs) do not take explicit forms. We approximate the likelihood equations and derive explicit estimators of the parameters. The bias and variance of the estimators are investigated and Monte Carlo simulation studies show that the estimators are as efficient as the classic MLEs. We demonstrate that the probability coverages of the pivotal quantities (for location and scale parameters) based on asymptotic normality are unsatisfactory, especially when the sample size is small. The use of unconditional simulated percentage points of these quantities is suggested. Finally, a numerical example is used to illustrate the proposed inference methods.     

On one twoepoch linear model with the nuisance parameters

The optimum linear estimators of the useful mean value parameters within a linear regression model with the stable and variable parameters and with the nuisance parameters are derived including their characteristics of accuracy. Some verification of theoretical results is presented.      

Maximum Likelihood Estimation of Asymmetric Laplace Parameters

Maximum likelihood estimators (MLE's) are presented for the parameters of a univariate asymmetric Laplace distribution for all possible situations related to known or unknown parameters. These estimators admit explicit form in all but two cases. In these exceptions effective algorithms for computing the estimators are provided. Asymptotic distributions of the estimators are given. The asymptotic normality and consistency of the MLE's for the scale and location parameters are derived directly via representations of the relevant random variables rather than from general sufficient conditions for asymptotic normality of the MLE's.     

基于均匀分布参数估计的几个结果

在总体分布为U(0,θ)和U(1θ,2θ)下,给出了未知参数θ,1θ,2θ的一些点估计量,并讨论了这些估计量的性质,对原有结果进行了补充.     

Log-logistic parameters estimation using moving extremes ranked set sampling design

In statistical parameter estimation problems, how well the parameters are estimated largely depends on the sampling design used. In the current paper, a modification of ranked set sampling(RSS) called moving extremes RSS(MERSS) is considered for the estimation of the scale and shape parameters for the log-logistic distribution. Several traditional estimators and ad hoc estimators will be studied under MERSS. The estimators under MERSS are compared to the corresponding ones under SRS. The simulation results show that the estimators under MERSS are significantly more efficient than the ones under SRS.     

二元Friday-Patil型指数分布的特征及其应用

导出了二元Friday-Patil型指数分布的一个特征,利用该特征获得了二元Friday-Patil型指数分布参数的最大似然估计及矩估计,给出了强度服从二元Friday-Patil型指数分布时系统可靠度的估计.     

An admissible minimax estimator of a bounded scale-parameter in a subclass of the exponential family under scale-invariant squared-error loss

A subclass of the scale-parameter exponential family is considered and for the rth power of the scale parameter, which is lower bounded, an admissible minimax estimator under scale-invariant squared-error loss is presented. Also, an admissible minimax estimator of a lower-bounded parameter in the family of transformed chi-square distributions is given. These estimators are the pointwise limits of a sequence of Bayes estimators. Some examples are given.