General admissibility for linear estimators in a general multivariate linear model under balanced loss function

A generalization of Zellner’s balanced loss function is proposed. General admissibility in a general multivariate linear model is investigated under the generalized balanced loss function. And the sufficient and necessary conditions for linear estimators to be generally admissible in classes of homogeneous and nonhomogeneous linear estimators are given, respectively.     

Admissibility of Confidence Estimators in the Regression Model

In the regression model, we assume that the independent variables are random instead of fixed. Consider the problem of estimating the coverage function of a usual confidence interval for the unknown intercept parameter. In this paper, we consider a case in which the number of unknown parameters is smaller than 5. We show that the usual constant coverage probability estimator is admissible in the usual sense in this case. Note that this estimator is inadmissible in the usual sense in the other case where the number of unknown parameters is greater than 4.     

矩阵损失下一般Gauss-Markov模型线性预测的可容许性

本文研究了一般Gauss-Markov模型中线性可预测变量的线性预测的可容许性.在给出线性预测可容许性定义的基础上,通过构造一个特殊的常量矩阵D0,分别得到了齐次和非齐次线性预测类中可容许的充要条件.     

The discrete coagulation-fragmentation equations: Existence,uniqueness, and density conservation

The discrete coagulation-fragmentation equation describes the kinetics of cluster growth in which clusters can coagulate via binary interactions to form larger clusters or fragment to form smaller ones. These models have many applications in pure and applied science ranging from cluster formation in galaxies to the kinetics of phase transformations in binary alloys. Our results relate to existence, uniqueness, density conservation and continuous dependence and they generalise the corresponding results in [ref. 2] for the Becker-Doring equations for which the processes are restricted to clusters gaining or shedding one particle. Examples are given which illustrate the role of the assumptions on the kinetic coefficients and show the rich set of analytic phenomena supported by the general discrete coagulation-fragmentation equations.     

多元线性模型中的有偏估计

刘金山在1999年给出了多元线性模型参数分量βi和参数矩阵B的有偏估计β1=(X'X)-1YCi,i=1,…,m和B=(β1,β2,…,βm)以及βi的性质.本文从另一角度得到了同样的估计,证明了刘金山文中所给的两个检验是UMP检验,估计βi是βi的线性可容许估计,证明了B不是B的可容许估计,由此给出了两种改进估计.     

椭球约束下误差方差非负二次估计的可容许性

本文给出了线性模型中椭球约束下，误差方差非负二次估计可容许的一个必要条件，并且，对于线性模型中设计阵X＝1nj=(1,1,…，1）′的特殊情形，本文给出了一个充要条件。     

A Class of Linear Biased Estimators of Regression ParameterMatrix in the Growth Curve Model

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一类独立随机变量均值中参数的估计

本文给出了独立随机变量均值中参数ａ＝（ａ１，…，ａｐ）′的估计量（ａ１Ｘ１，…，ａｐＸｐ）′在加权平方和损失下为可容许估计的充要条件及在一般损失Ｌｖ下为可容许估计的充分条件（在线性估计类中）。