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.     

Nonparametric control charts based on runs and Wilcoxon-type rank-sum statistics

In this article, we introduce three new distribution-free Shewhart-type control charts that exploit run and Wilcoxon-type rank-sum statistics to detect possible shifts of a monitored process. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of these charts is that, due to their nonparametric nature, the false alarm rate (FAR) and in-control run length distribution is the same for all continuous process distributions. Tables are provided for the implementation of the charts for some typical FAR values. Furthermore, a numerical study carried out reveals that the new charts are quite flexible and efficient in detecting shifts to Lehmann-type out-of-control situations.     

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.     

Partial least squares estimator for single-index models

The partial least squares (PLS) approach first constructs new explanatory variables, known as factors (or components), which are linear combinations of available predictor variables. A small subset of these factors is then chosen and retained for prediction. We study the performance of PLS in estimating single-index models, especially when the predictor variables exhibit high collinearity. We show that PLS estimates are consistent up to a constant of proportionality. We present three simulation studies that compare the performance of PLS in estimating single-index models with that of sliced inverse regression (SIR). In the first two studies, we find that PLS performs better than SIR when collinearity exists. In the third study, we learn that PLS performs well even when there are multiple dependent variables, the link function is non-linear and the shape of the functional form is not known.     

论行政道德建设的运行机制

坚持行政目标管理与行政道德要求、精神激励与物质激励、政策保障与经济保障、领导与群众、法治与德治、全过程监督与全方位监督的相结合,从而建立并健全考核机制、激励机制、保障机制、互动机制、规范机制和监督机制是促进行政道德建设健康发展的根本措施。     

湖南文学百年兴衰溯源：－兼评田中阳《湖湘文化精神与二十世纪湖南文学》

政治本位的近世湖湘文化在中国近、现代史中曾独领一代风骚,然而在当代却遭遇了从极盛走向衰朽的命运湖南文学的百年盛衰,也恰恰能够从湖湘文化精神本身的优长与历史局限中找到潜因.20世纪湖南作家创作心理定势及其创作文本思想倾向、艺术特质都受到了湖湘文化深刻的影响和规约.田中阳之新著<湖湘文化精神与二十世纪湖南文学>便对这两者之间的深刻关联进行了富有创见性的精要论述.     

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。     

新形势下坚持党的先进性的科学抉择

在新时期 ,我们应正确认识无产阶级政党的先进性与党员成份之间的科学关系 ;明确吸收新的社会阶层中的优秀分子入党是建设有中国特色社会主义伟大事业的必然要求 ;有利于进一步巩固党的工人阶级先锋队性质。