Identifying Nonlinear Relationships in Regression using the ACE Algorithm

This paper introduces an alternating conditional expectation (ACE) algorithm: a non-parametric approach for estimating the transformations that lead to the maximal multiple correlation of a response and a set of independent variables in regression and correlation analysis. These transformations can give the data analyst insight into the relationships between these variables so that this can be best described and non-linear relationships uncovered. Using the Bayesian information criterion (BIC), we show how to find the best closed-form approximations for the optimal ACE transformations. By means of ACE and BIC, the model fit can be considerably improved compared with the conventional linear model as demonstrated in the two simulated and two real datasets in this paper.     

Generalized Self-Consistency: Multinomial logit model and Poisson likelihood

A generalized self-consistency approach to maximum likelihood estimation (MLE) and model building was developed in Tsodikov [2003. Semiparametric models: a generalized self-consistency approach. J. Roy. Statist. Soc. Ser. B Statist. Methodology 65(3), 759–774] and applied to a survival analysis problem. We extend the framework to obtain second-order results such as information matrix and properties of the variance. Multinomial model motivates the paper and is used throughout as an example. Computational challenges with the multinomial likelihood motivated Baker [1994. The Multinomial–Poisson transformation. The Statist. 43, 495–504] to develop the Multinomial–Poisson (MP) transformation for a large variety of regression models with multinomial likelihood kernel. Multinomial regression is transformed into a Poisson regression at the cost of augmenting model parameters and restricting the problem to discrete covariates. Imposing normalization restrictions by means of Lagrange multipliers [Lang, J., 1996. On the comparison of multinomial and Poisson log-linear models. J. Roy. Statist. Soc. Ser. B Statist. Methodology 58, 253–266] justifies the approach. Using the self-consistency framework we develop an alternative solution to multinomial model fitting that does not require augmenting parameters while allowing for a Poisson likelihood and arbitrary covariate structures. Normalization restrictions are imposed by averaging over artificial “missing data” (fake mixture). Lack of probabilistic interpretation at the “complete-data” level makes the use of the generalized self-consistency machinery essential.     

A comparison of methods for the fitting of generalized additive models

There are several procedures for fitting generalized additive models, i.e. regression models for an exponential family response where the influence of each single covariates is assumed to have unknown, potentially non-linear shape. Simulated data are used to compare a smoothing parameter optimization approach for selection of smoothness and of covariates, a stepwise approach, a mixed model approach, and a procedure based on boosting techniques. In particular it is investigated how the performance of procedures is linked to amount of information, type of response, total number of covariates, number of influential covariates, and extent of non-linearity. Measures for comparison are prediction performance, identification of influential covariates, and smoothness of fitted functions. One result is that the mixed model approach returns sparse fits with frequently over-smoothed functions, while the functions are less smooth for the boosting approach and variable selection is less strict. The other approaches are in between with respect to these measures. The boosting procedure is seen to perform very well when little information is available and/or when a large number of covariates is to be investigated. It is somewhat surprising that in scenarios with low information the fitting of a linear model, even with stepwise variable selection, has not much advantage over the fitting of an additive model when the true underlying structure is linear. In cases with more information the prediction performance of all procedures is very similar. So, in difficult data situations the boosting approach can be recommended, in others the procedures can be chosen conditional on the aim of the analysis.     

“双元结构”下的概念转换

由于中国成年人在学习外语时有"双元结构"的存在,因而造成了成年人在进行语义理解时对不同语言的不同原型不能理解和转换,这时就需要借助概念进行转换,而在概念转换时激活不同文化模式下认知域,从而达到匹配语义、理解语义的目的,当不能匹配时,就需文化的介入,进而完成概念转换.     

先进文化和中国文学的文化转型

由于改革开放以后经济模式的转变,中国社会正处于转型阶段。从先秦时代就传承而下的中国传统文化先进观念——现实观、平等观和大同观对中国文学产生了巨大的影响,并将指导中国文学走出文化转型的困境。     

Estimation method of multivariate exponential probabilities based on a simplex coordinates transform

A novel unbiased estimator for estimating the probability mass of a multivariate exponential distribution over a measurable set is introduced and is called the exponential simplex (ES) estimator. For any measurable set and given sample size, the statistical efficiency of the ES estimator is higher than or equal to the statistical efficiency of the well-known Monte Carlo (MC) estimator. For non-radially shaped measurable sets, the ES estimator has a strictly higher statistical efficiency than the MC estimator. For ray-convex sets, such as convex sets, the ES estimator can be expressed in a simple analytical form.     

On the Ghoudi,Khoudraji, and Rivest test for extreme‐value dependence

Ghoudi, Khoudraji & Rivest [The Canadian Journal of Statistics 1998;26:187–197] showed how to test whether the dependence structure of a pair of continuous random variables is characterized by an extreme‐value copula. The test is based on a U‐statistic whose finite‐ and large‐sample variance are determined by the present authors. They propose estimates of this variance which they compare to the jackknife estimate of Ghoudi, Khoudraji & Rivest ( 1998 ) through simulations. They study the finite‐sample and asymptotic power of the test under various alternatives. They illustrate their approach using financial and geological data. The Canadian Journal of Statistics © 2009 Statistical Society of Canada     

深圳特区制度的历史实证分析及未来展望

本文以新制度经济学的相关理论为基础，分析深圳特区制度的形成过程，提出了深圳制度优势形成的特点，即由国家政策、地缘优势和移民城市构成的制度形成模式。然后通过对政府效率的实证分析，说明深圳与国内其他城市相比，确实存在制度优势。同时，也指出深圳在制度变迁过程中存在的一些不足及原因。本文认为，今后深圳应该在原有的制度形成模式基础上，建立以完善社会主义市场经济体制试验区为目标的制度框架，以继续发挥特区的制度优势，顺利实现城市发展转型。     

Better Articulating Normal Curve Theory for Introductory Mathematical Statistics Students: Power Transformations and Their Back-Transformations

This article addresses a gap in many, if not all, introductory mathematical statistics textbooks, namely, transforming a random variable so that it better mimics a normal distribution. Virtually all such textbooks treat the subject of variable transformations, which furnishes a nice opportunity to introduce and study this transformation-to-normality topic, a topic students frequently encounter in subsequent applied statistics courses. Accordingly, this article reviews variable power transformations of the Box–Cox type within the context of normal curve theory, as well as addresses their corresponding back-transformations. It presents four theorems and a conjecture that furnish the basics needed to derive equivalent results for all nonnegative values of the Box–Cox power transformation exponent. Results are illustrated with the exponential random variable. This article also includes selected pedagogic tools created with R code.     

文明转型时期的中国理论思维建设

工业文明是第一个影响和支配了全世界的人类文明形态，但不是所有民族共享的文明形态。信息—生态文明将是全人类共享的第一个文明形态。现在，人类正处于从工业文明向信息—生态文明转变的历史时期。在这次文明转型中，如何规划我国的理论思维建设极为重要。我们必须以建设信息—生态文明为参照系，重新解读马克思，解读当代世界的实际演进，重读、改造和发展我们的传统文化