读朱新天著《印度教万神殿艺术——印度王后井探秘》

朱新天博士的新著《印度教万神殿艺术——印度王后井探秘》,是她近20年来苦心研究印度艺术的结晶。该书已分别以中、英、法三种文字同时出版,在国际印度艺术研究领域产生了重要影响。     

金融危机下中国创业投资“囚徒困境”演化研究

创业投资家和创业企业家的＂囚徒困境＂是制约中国创业投资进一步发展的主要障碍之一。对短期利益的追求和缺乏信任是造成中国创业投资＂囚徒困境＂的两个重要原因。在金融危机背景下,＂囚徒困境＂的演化将朝着有利于创业投资家的方向发展。金融危机虽然能改变博弈的结果,却未能改变＂囚徒困境＂的成因。     

简论语料库与教师角色之转变

现代电子语料库已有了近50年的发展,但语料库应用于课堂教学才刚刚起步。通过近年语料库辅助课堂教学诸多实践研究,教师们不仅可以获得教学中的例句,还可引导学生们学习更地道、更准确的表达方式。     

数据挖掘中关联规则的规范化描述

一、引言数据挖掘(Data Mining)是近年来随着人工智能和数据库技术的发展而出现的一门新兴学科。它是从大量的数据中筛选出隐含的、可信的、新颖的、有效的信息的高级处理过程。关联规则(Association Rule)是其中重要的研究课题,是数据挖掘的主要技术之一,也是在无指导学习系统     

初等树变换的算法改造

本文利用王氏代数对用初等树变换生成树的方法进行了改造,提出了一种新的初等树变换的算法。新算法较之原法简洁、直观、运算方便、概念清楚,并保留了原法的所有优点。     

关于平面对称紧凸集不等式

本文简论平面对称紧凸集不等式问题,引伸Favard不等式,对不等式中的相关常数给出两种证法。     

Measuring non-linear dependence for two random variables distributed along a curve

We propose new dependence measures for two real random variables not necessarily linearly related. Covariance and linear correlation are expressed in terms of principal components and are generalized for variables distributed along a curve. Properties of these measures are discussed. The new measures are estimated using principal curves and are computed for simulated and real data sets. Finally, we present several statistical applications for the new dependence measures.     

Regularization through variable selection and conditional MLE with application to classification in high dimensions

It is often the case that high-dimensional data consist of only a few informative components. Standard statistical modeling and estimation in such a situation is prone to inaccuracies due to overfitting, unless regularization methods are practiced. In the context of classification, we propose a class of regularization methods through shrinkage estimators. The shrinkage is based on variable selection coupled with conditional maximum likelihood. Using Stein's unbiased estimator of the risk, we derive an estimator for the optimal shrinkage method within a certain class. A comparison of the optimal shrinkage methods in a classification context, with the optimal shrinkage method when estimating a mean vector under a squared loss, is given. The latter problem is extensively studied, but it seems that the results of those studies are not completely relevant for classification. We demonstrate and examine our method on simulated data and compare it to feature annealed independence rule and Fisher's rule.     

Another look at Huber's estimator: A new minimax estimator in regression with stochastically bounded noise

Huber's estimator has had a long lasting impact, particularly on robust statistics. It is well known that under certain conditions, Huber's estimator is asymptotically minimax. A moderate generalization in rederiving Huber's estimator shows that Huber's estimator is not the only choice. We develop an alternative asymptotic minimax estimator and name it regression with stochastically bounded noise (RSBN). Simulations demonstrate that RSBN is slightly better in performance, although it is unclear how to justify such an improvement theoretically. We propose two numerical solutions: an iterative numerical solution, which is extremely easy to implement and is based on the proximal point method; and a solution by applying state-of-the-art nonlinear optimization software packages, e.g., SNOPT. Contribution: the generalization of the variational approach is interesting and should be useful in deriving other asymptotic minimax estimators in other problems.     

On the asymptotic distribution of Cook's distance in logistic regression models

It sometimes occurs that one or more components of the data exert a disproportionate influence on the model estimation. We need a reliable tool for identifying such troublesome cases in order to decide either eliminate from the sample, when the data collect was badly realized, or otherwise take care on the use of the model because the results could be affected by such components. Since a measure for detecting influential cases in linear regression setting was proposed by Cook [Detection of influential observations in linear regression, Technometrics 19 (1977), pp. 15–18.], apart from the same measure for other models, several new measures have been suggested as single-case diagnostics. For most of them some cutoff values have been recommended (see [D.A. Belsley, E. Kuh, and R.E. Welsch, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, 2nd ed., John Wiley & Sons, New York, Chichester, Brisban, (2004).], for instance), however the lack of a quantile type cutoff for Cook's statistics has induced the analyst to deal only with index plots as worthy diagnostic tools. Focussed on logistic regression, the aim of this paper is to provide the asymptotic distribution of Cook's distance in order to look for a meaningful cutoff point for detecting influential and leverage observations.