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.     

Cumulative correspondence analysis of ordered categorical data from industrial experiments

Most studies of quality improvement deal with ordered categorical data from industrial experiments. Accounting for the ordering of such data plays an important role in effectively determining the optimal factor level of combination. This paper utilizes the correspondence analysis to develop a procedure to improve the ordered categorical response in a multifactor state system based on Taguchi's statistic. Users may find the proposed procedure in this paper to be attractive because we suggest a simple and also popular statistical tool for graphically identifying the really important factors and determining the levels to improve process quality. A case study for optimizing the polysilicon deposition process in a very large-scale integrated circuit is provided to demonstrate the effectiveness of the proposed procedure.     

论中国共产党建党理论的创新

实践证明,党的建设是我们党克敌制胜的一大法宝,而建党理论的创新是前提。中国共产党把马克思列宁主义建党理论同中国实际相结合,提出适合中国国情的党的建设理论,反映了时代的需要,全面体现了党的先进性,增强了党的凝聚力和战斗力。学习掌握这些经验,对于我们坚持新时期党的建设纲领有着重要意义。     

从康德道德文化看圆善之铸成——读《圆善论》

康德在《纯然理性限度内的宗教》一书中,论述了人性中原初的善、人性中根本的恶、人的堕落、人的重新向善、道德寻求宗教等内容,尤其是康德"至善"的思想对牟宗三影响很大,牟宗三受到启发创作《圆善论》,重铸儒家道德理想主义。尝试通过梳理康德思想内涵,逐步引出牟宗三的圆教与圆善思想,从而发现此二者之间思想精髓的内在的一致性。     

《政治经济学批判大纲》的哲学性质

在马克思主义哲学的创立过程中,恩格斯的《政治经济学批判大纲》具有特殊的地位和作用。就其哲学的性质,中外哲学界存在着许多不同的看法,这些不同的看法,直接影响着人们对马克思主义哲学的实质的理解。我们认为,恩格斯在《政治经济学批判大纲》中所表现出的哲学立场,一方面表明他完成了从唯心主义向唯物主义的根本转变,另一方面也表明,恩格斯此时的哲学世界观还停留在"费尔巴哈派"的阶段。     

理性的灵魂 智慧的结晶———钟光荣经济哲学理论对当代社会经济发展的启示

钟光荣的经济哲学思想和理论给我们的启示,归结起来,就是能够使我们看到：人类社会发展中出现的所有经济垢病,都是人为经济灾害;造成人为经济灾害的根本原因,是传统经济学的价值理论错觉所引致的社会经济实践错行.要从根本上消除这一经济知行之错,现代经济学就必须努力开显自然经济的真理和法则,并建立符合这个真理和法则的经济发展模式,以其对人们的经济知行进行约束和规范.但要使这种约束和规范行之有效,最根本的措施,就是培养人们效法自然博爱的道德理性.     

马克思主义的幸福观及其中国化何以可能——基于“中国梦”人民幸福内涵的理论渊源及实践价值视角

关于"中国梦"人民幸福内涵的历史渊源及实践价值研究,必然涉及中国化的马克思主义幸福观存在依据和理论形态等问题。马克思主义幸福观中国化何以可能?这一追问实际包含了两个问题:第一,在实际上是否存在马克思主义幸福观,其是否具有合理性。它与现在我们在非严格意义上使用的"马克思幸福观"是否应该有所区别。第二,中国革命为什么需要马克思主义幸福观中国化?这一命题所指称的过程是否真正发生过。科学的马克思主义幸福观,就是符合马克思主义幸福观本来面目和本质特性的关于马克思主义幸福观认知和评价问题上的根本态度与根本观点,应该包括马克思的伦理幸福观、哲学幸福观和人民的现实幸福论。哲学幸福观在马克思主义幸福观中居于核心地位,幸福本质观是马克思主义哲学幸福观的核心内容。幸福首先是一个关于人的本体论问题,不能仅以道德来界定幸福的内涵。实践本体论是马克思主义哲学幸福观产生的母体,将唯心主义的幸福观改造成实践唯物主义的幸福观,将幸福感作为成功的社会实践活动的结果和必要环节。人民的现实幸福论是马克思的幸福本质论革命的主要成果和标志,从关注现实人的幸福本身转向探求人民的现实幸福实现的途径和条件,经历了从劳动幸福观到实践幸福观的过渡。"人民的现实幸福论"具体化、中国化就是马克思主义幸福观中国化的主要内涵和基本路径,"中国特色"人民的现实幸福论是中国特色社会主义幸福理论的基本存在形态及表现形式,是马克思主义幸福观中国化的理论成果之核心内容。"中国梦"蕴含的"人民幸福"思想的理论创新则是"人民幸福本位"思想的不断深化和大众化。