Robustness of the linear discriminant function to nonnormality: Johnson's system

The asymptotic distribution of the Errors of Misclassification in using the Linear Discriminant Function is investigated here. The purpose is to study the effects of nonnormality on these errors. The class of distributions considered is the Johnson's system. Each of the three random variables can be transformed to normality. In one particular case numerical evaluations are made, based on which it is possible to recommend whether or not it is necessary to make the transformation prior to classification. In a parallel study, we present similar results for the Edgeworth Series distribution, where the random variables cannot be transformed to normality.     

综合性大学发展师范教育的困境及其解决途径

20世纪90年代以来出现了高校合并的浪潮,在此次浪潮的影响下,各综合性大学纷纷建立教育学院、师范学院、教育系或开设教育类课程,承担起为中等教育培养师资的重任,为师范教育的发展带来了良好的机遇。但是,在综合性大学开展师范教育也存在着管理体制不完善、师资力量不足、培养目标不明确、课程设置僵化等缺陷,要从根本上解决这些问题,加强综合性大学中师范教育的“师范性”,就必须在推进制度化建设、优化教师队伍、促进师范专业学科建设、创新培养模式、开设校本化课程等方面下功夫,以适应高教改革,推动师范教育的发展。     

川东师范学堂与西南师范学院的组建

为实施新学制,培养师资,光绪三十二年(1906年)重庆创办了第一所正规的师范学校--官立川东师范学堂.民国建立后,该学堂改名为川东师范学校.1932年,该校设立乡村师范专修科.次年,专修科迁至沙坪坝磁器口,并先后改名为乡村建设学院、四川省立教育学院.1950年,四川省立教育学院与1940年创办的国立女子师范学院合并组建西南师范学院.1985年,西南师范学院更名为西南师范大学.     

LOGISTIC REGRESSION COMPARED TO NORMAL DISCRIMINATION FOR NON-NORMAL POPULATIONS'

An investigation is undertaken of the logistic regression procedure for estimating the posterior probability of an object belonging to one of two populations. The asymptotic bias and mean square error associated with the procedure are derived for univariate populations whose distributions satisfy the general Day-Kerridge model for which the logistic form is valid for the posterior probability. These properties are compared with those of the normal discrimination method based on the classical assumption of normal populations with common variances. The asymptotic relative efficiency of logistic regression is considered on the basis of asymptotic mean square error.     

广西幼儿师范学校“3+2”学前教育专业课程的设计与实施

经过多年的实践,广西幼儿师范学"校3+2"学前教育专业课程设计的指导思想基本明确,培养目标逐渐回归现实基础,课程特色鲜明,但也还存在一些值得进一步探讨的问题。     

A Bayesian Learning Coefficient of Generalization Error and Vandermonde Matrix-Type Singularities

The coefficient of the main term of the generalization error in Bayesian estimation is called a Bayesian learning coefficient. In this article, we first introduce Vandermonde matrix type singularities and show certain orthogonality conditions of them. Recently, it has been recognized that Vandermonde matrix type singularities are related to Bayesian learning coefficients for several hierarchical learning models. By applying the orthogonality conditions of them, we show that their log canonical threshold also corresponds to the Bayesian learning coefficient for normal mixture models, and we obtain the explicit computational results in dimension one.     

On Sharp Jensen's Inequality and Some Unusual Applications

The purpose of this article is two-fold. First, we find it very interesting to explore a kind of notion of optimality of the customary Jensen-bound among all Jensen-type bounds. Without this result, the customary Jensen-bound stood alone simply as just another bound. The proposed notion and the associated optimality are important given that in some situations the Jensen's inequality does leave us empty handed.

When it comes to highlighting Jensen's inequality, unfortunately only a handful of nearly routine applications continues to recycle time after time. Such encounters rarely produce any excitement. This article may change that outlook given its second underlying purpose, which is to introduce a variety of unusual applications of Jensen's inequality. The collection of our important and useful applications and their derivations are new.     

Normal Deviation and Poisson Approximation of a Security Market by the Geometric Markov Renewal Processes

We consider the geometric Markov renewal processes (GMRP) as a model for a security market. Normal deviations of the geometric Markov renewal processes for ergodic averaging and double averaging schemes are derived. We introduce Poisson averaging scheme for the geometric Markov renewal processes. European call option pricing formulas for GMRP are presented.     

Objective Priors for Parameters in a Normal Linear Regression with Measurement Error

We investigate certain objective priors for the parameters in a normal linear regression models with one of the explanatory variables subject to measurement error. We first show that the use of the standard non informative prior for normal linear regression without measurement error leads to an improper posterior in the measurement error model. We then derive the Jeffreys prior and reference priors, and show that they lead to proper posteriors. We use simulation study to compare the frequentist performance of the estimates derived using these priors, and the MLE.     

Interval Estimation of the Stress-Strength Reliability with Independent Normal Random Variables

This article develops a procedure to obtain highly accurate confidence interval estimates for the stress-strength reliability R = P(X > Y) where X and Y are data from independent normal distributions of unknown means and variances. Our method is based on third-order likelihood analysis and is compared to the conventional first-order likelihood ratio procedure as well as the approximate methods of Reiser and Guttman (1986 Reiser, B., Guttman, I. (1986). Statistical inference for Pr(Y < X): the normal case. Technometrics 28: 253257.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Guo and Krishnamoorthy (2004 Guo, H., Krishnamoorthy, K. (2004). New approximate inferential methods for the reliability parameter in a stress-strength model: the normal case. Commun. Statist. Theor. Meth. 33: 17151731.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The use of our proposed method is illustrated by an empirical example and its superior accuracy in terms of coverage probability and error rate are examined through Monte Carlo simulation studies.