关于预测误差平方和最小准则的几点看法

在应用桃棣荣等提出的预测误差平方和（ＰＲＥＳＳ）最小准则逐步算法的过程中，发现单纯应用ＰＲＥＳＳ值来控制引进因子数目有时不很有效。因此建议：１）当引进因子过多时，采用赤池信息准则对因子数做进一步控制。２）当引进因子过少时，取消原算法中关于ＰＲＥＳＳ值上界的规定和增加候选因子数以增加引进因子数。最后，对应用ＰＲＥＳＳ准则时所选因子的优良性进行了讨论     

MARS: selecting basis functions and knots with an empirical Bayes method

An empirical Bayes method to select basis functions and knots in multivariate adaptive regression spline (MARS) is proposed, which takes both advantages of frequentist model selection approaches and Bayesian approaches. A penalized likelihood is maximized to estimate regression coefficients for selected basis functions, and an approximated marginal likelihood is maximized to select knots and variables involved in basis functions. Moreover, the Akaike Bayes information criterion (ABIC) is used to determine the number of basis functions. It is shown that the proposed method gives estimation of regression structure that is relatively parsimonious and more stable for some example data sets.     

基于属性测度的决策系统研究

在属性集和属性测度理论基础上系统地讨论了属性测度综合评价和决策系统.把综合决策系统分为三个子系统;第一个为单指标性能函数分析子系统,第二个为多指标综合性能函数分析子系统;第三个为识别分析子系统.并在属性测度决策系统的基础上,给出了一个应用实例.通过实例的分析,表明该系统是合理、实用和有效的.     

On spline approximation of sliced inverse regression

The dimension reduction is helpful and often necessary in exploring the nonparametric regression structure.In this area,Sliced inverse regression (SIR) is a promising tool to estimate the central dimension reduction (CDR) space.To estimate the kernel matrix of the SIR,we herein suggest the spline approximation using the least squares regression.The heteroscedasticity can be incorporated well by introducing an appropriate weight function.The root-n asymptotic normality can be achieved for a wide range choice of knots.This is essentially analogous to the kernel estimation.Moreover, we also propose a modified Bayes information criterion (BIC) based on the eigenvalues of the SIR matrix.This modified BIC can be applied to any form of the SIR and other related methods.The methodology and some of the practical issues are illustrated through the horse mussel data.Empirical studies evidence the performance of our proposed spline approximation by comparison of the existing estimators.     

An Oscillation Criterion for Second Order Superlinear Differential Equations

61.IntroductionConsiderthesecondordersuperlinearequationx'(t) p(t)X'(t) q(t)1x(t)l"sgnx(t)=o,t>to,(1)wherea>l,pandq:[t,'co)-R=(-co,oo)arecontinuous.Weconsideronlysuchsolutionsxofequation(l)whichexistonsomeinterval[t.,oo),t.>t,>o.Asolutionofequation(l)issaidtobeoscillatoryifithasarbitrarilylargezerosandotherwise,itissaidtobenonoscillatory.Equation(l)iscalledoscillatoryifallofitssolutionsareoscilllatory.Forthespecialcasewherep(t)=Oli.e.,forthedifferentialequationx'(t) q(t)lx(t)l"sgnx(t)=o,a>1-…     

LR test for random-effects covariance structure in a parallel profile model

We consider a parallel profile model which is useful in analyzing parallel growth curves of several groups. The likelihood ratio criterion for a hypothesis concerning the adequacy of a random-effects covariance structure is obtained under the parallel profile model. The likelihood ratio criterion for the hypothesis in the general one-way MANOVA model is also obtained. Asymptotic null distributions of the criteria are derived when the sample size is large. We give a numerical example of these asymptotic results.     

On certain spectral properties of a quadratic self-adjoint matrix pencil with dominating main diagonals

Sufficient conditions for the “separation of the spectrum” of a quadratic matrix pencil with self-adjoint coefficients are found. A criterion for the representability of a positive operator in a finite-dimensional space in the form of a matrix with dominating main diagonal in each orthonormal basis is obtained. Translated fromMatematicheskie Zametki, Vol. 61, No. 3, pp. 381–390, March, 1997. Translated by A. I. Shtern     

以LCD为目标的自动定焦判据选择

在光学综合自动测量中 ,使用液晶显示屏作为分划板可以大大简化结构 ,提高效率 ,真正地实现自动测量。由于液晶显示具有对比度低、噪声大等特点 ,所以根据液晶的这些特点以及图像处理和CCD信号接收的特点选择两种适用的判据进行了分析和试验比较 ,并给出了结果。结果表明 ,这两种判别函数都适用于以液晶显示屏为目标和用图像处理方法进行光学参数测量的系统 ,其中锐度判别函数更优于信息熵判别函数 ,前者具有更好的抗干扰性和稳定性 ,而且其判定结果更接近目视清晰度判别     

报酬无界的平均准则马氏决策过程

本文对可数状态集、非空决策集、报酬无界的平均准则马氏决策过程，提出了一组新的条件，在此条件下存在（ε）最优平稳策略，且当最优不等式中的和有定义时最优不等式也成立。     

Thermal explosion in multiple phase media

Thermal explosion (or self-ignition) is one of the mainly interesting and dangerous phenomena in the combustion. Homogeneous combustible gas mixtures with highly exothermic reaction reveal only two main types of the behaviour: explosive and slow. Transient regime between these main types of behaviour is traditionally called the thermal explosion limit. Addition of another phase (solid or liquid) into combustible gas mixture can lead to essential changes in the dynamical situation. This paper deals with an interesting phenomenon of thermal explosion in two-phase media, so-called thermal explosion with delay. Existence and type of temperature delay before the self-ignition depends on mass and thermal properties of the second phase. The analysis is based on qualitative theory of singular perturbed systems and duck techniques.