Comparisons among regression estimators under the generalized mean square error criterion

It is not always prossible to establish a preference ordering among regression estimators in terms of the generalized mean square error criterion. In the paper, we determine when it is feasible to use this criteion to couduct comparisons among ordinary least squares, principal components, ridge regression, and shrunken least squares estimators.     

Uncertainty Importance Analysis Using Parametric Moment Ratio Functions

This article presents a new importance analysis framework, called parametric moment ratio function, for measuring the reduction of model output uncertainty when the distribution parameters of inputs are changed, and the emphasis is put on the mean and variance ratio functions with respect to the variances of model inputs. The proposed concepts efficiently guide the analyst to achieve a targeted reduction on the model output mean and variance by operating on the variances of model inputs. The unbiased and progressive unbiased Monte Carlo estimators are also derived for the parametric mean and variance ratio functions, respectively. Only a set of samples is needed for implementing the proposed importance analysis by the proposed estimators, thus the computational cost is free of input dimensionality. An analytical test example with highly nonlinear behavior is introduced for illustrating the engineering significance of the proposed importance analysis technique and verifying the efficiency and convergence of the derived Monte Carlo estimators. Finally, the moment ratio function is applied to a planar 10‐bar structure for achieving a targeted 50% reduction of the model output variance.     

广义次正定矩阵

定义了广义次正定矩阵，研究了广义次正定矩阵的一些性质，给出了判定ｎ阶矩阵是广义次正定矩阵的一系列充要条件     

词义及其构成研究拾零

词义及构成研究中遗留着许多问题,需要深入探讨。语义三角理论对宏观上的词义认知具有重要价值。词义是复合的结构体。语法义在词义结构中具有普遍性;概念义是词义的基础,是理性义的一种主要类型。     

永恒的主题:人为和自然的对比——评简·奧斯汀的《傲慢与偏见》

《傲慢与偏见》虽然在表面上缺乏时代特点,却间接地通过对外在的人为价值和内在的自然价值间的矛盾冲突的描写,从人的精神层次上反映了一个变革的时代。而这种矛盾冲突对比的描写尤其表现在主要人物的刻画和情节展开上。因而通过对作品中主要人物和情节的分析可以看到,奧斯汀对于极端的追求人为价值持否定的态度,而对于单纯的追求人的自然价值也是不能完全认同。她认为最理想的解决办法就是走折衷的道路。     

存在融资条件下证券组合选择的一种模糊决策方法

应用模糊可能性理论研究了在实际投资决策中存在融资条件下的证券组合选择问题。用证券收益的可能性均值和方差分别作为投资收益和风险的测度，将选择证券组合的概率均值一方差模型简化为一个线性规划模型，使得存在融资条件下有效投资组合的算法问题得到解决。最后，给出了一个数值例子，说明了这种决策方法是便捷有效的。     

具耗散项的对称正则长波方程的定性分析及显式解

运用常微分方程定性理论中的相平面分析方法讨论了具耗散项的对称正则长波方程的行波解,得到了关于其有界行波解的存在性、单调性及振荡性的若干结果,并求出了一类扭状精确孤波解和振荡解的近似解.     

Efficiencies of six almost unbiased ratio estimators under a particular model

Efficiencies of six almost unbiased estimators for the ratio of population means of two characters, are compared under a linear regression model.     

A class of modified stein estimators with easily computable risk functions

Consider the problem of estimating the mean of a p (≥3)-variate multi-normal distribution with identity variance-covariance matrix and with unweighted sum of squared error loss. A class of minimax, noncomparable (i.e. no estimate in the class dominates any other estimate in the class) estimates is proposed; the class contains rules dominating the simple James-Stein estimates. The estimates are essentially smoothed versions of the scaled, truncated James-Stein estimates studied by Efron and Morris. Explicit and analytically tractable expressions for their risks are obtained and are used to give guidelines for selecting estimates within the class.     

The weighted likelihood

The authors consider a weighted version of the classical likelihood that applies when the need is felt to diminish the role of some of the data in order to trade bias for precision. They propose an axiomatic derivation of the weighted likelihood, for which they show that aspects of classical theory continue to obtain. They suggest a data‐based method of selecting the weights and show that it leads to the James‐Stein estimator in various contexts. They also provide applications.