Efficiency of the QR class estimator in semiparametric regression models to combat multicollinearity

There are some classes of biased estimators for solving the multicollinearity among the predictor variables in statistical literature. In this research, we propose a modified estimator based on the QR decomposition in the semiparametric regression models, to combat the multicollinearity problem of design matrix which makes the data to be less distorted than the other methods. We derive the properties of the proposed estimator, and then, the necessary and sufficient condition for the superiority of the partially generalized QR-based estimator over partially generalized least-squares estimator is obtained. In the biased estimators, selection of shrinkage parameters plays an important role in data analysing. We use generalized cross-validation criterion for selecting the optimal shrinkage parameter and the bandwidth of the kernel smoother. Finally, the Monté-Carlo simulation studies and a real application related to bridge construction data are conducted to support our theoretical discussion.     

Diagnostic measures for kernel ridge regression on reproducing kernel Hilbert space

The aim of this paper is to define and develop diagnostic measures with respect to kernel ridge regression in a reproducing kernel Hilbert space (RKHS). To identify influential observations, we define a particular version of Cook’s distance for the kernel ridge regression model in RKHS, which is conceptually consistent with Cook’s distance in a classical regression model. Then, by using the perturbation formula for the regularized conditional expectation of the outcome in RKHS, we develop an approximate version of Cook”s distance in RKHS because the original definition requires intensive computations. Such an approximated Cook”s distance is represented in terms of basic building blocks such as residuals and leverages of the kernel ridge regression. The results of the simulation and real application demonstrate that our diagnostic measure successfully detects potentially influential observations on estimators in kernel ridge regression.     

中国地区间教育不平等的分解及治理

采用中国1997—2008年的省级面板数据和夏普里值分解法对地区教育不平等进行分析,研究表明,发达地区教育发展的先发优势是导致地区教育不平等的重要原因,但其贡献度越来越小;各地财政性教育投入和经济发展之间的差异已成为影响地区教育不平等的最主要因素,二者的累计贡献率达60%以上。政府教育投入努力程度的贡献度有所降低,各地城市化差异的贡献度维持在10%左右。因此,应加大政府投入的水平和对落后地区的转移支付力度,提高教育的投入效率,提升地方政府发展教育的激励;通过提升城市化水平以实现城乡间、区域间教育的均衡发展。     

中国主要省份玉米价格的传导效应分析

文章选取2000-2011年玉米价格月度数据,采用向量自回归模型、脉冲效应函数以及方差分析等方法,研究省份玉米价格的传导效应,研究表明:主要省份玉米价格之间存在着双向的格兰杰因果关系,并存在长期的均衡关系;主要省份玉米价格冲击对本省玉米价格的波动最为明显,持续时间也较长,对于其他省份的影响则相对较弱;主销省份价格波动对于其他省份玉米价格波动所产生的影响高于主产省份,既是主产省,又是主销省的省份对于玉米价格波动的影响,明显高于主产省或主销省的影响。     

基于VAR模型的青岛市经济增长与环境污染的实证研究

通过以青岛市1985—2010年的人均GDP水平和主要污染物排放总量为样本建立向量自回归模型,并利用此模型对青岛市环境污染与经济增长之间的动态关系进行考察发现,经济增长会加速环境污染,由于环境承载力的存在,环境污染对经济的负面影响存在滞后期。作为山东半岛蓝色经济区的重要组成部分,青岛市必须加快优化产业和能源结构,大力发展海洋经济和循环经济,加快建设全国蓝色经济领军城市。     

A cautionary note on generalized linear models for covariance of unbalanced longitudinal data

Missing data in longitudinal studies can create enormous challenges in data analysis when coupled with the positive-definiteness constraint on a covariance matrix. For complete balanced data, the Cholesky decomposition of a covariance matrix makes it possible to remove the positive-definiteness constraint and use a generalized linear model setup to jointly model the mean and covariance using covariates (Pourahmadi, 2000). However, this approach may not be directly applicable when the longitudinal data are unbalanced, as coherent regression models for the dependence across all times and subjects may not exist. Within the existing generalized linear model framework, we show how to overcome this and other challenges by embedding the covariance matrix of the observed data for each subject in a larger covariance matrix and employing the familiar EM algorithm to compute the maximum likelihood estimates of the parameters and their standard errors. We illustrate and assess the methodology using real data sets and simulations.     

ORDANOVA: Analysis of ordinal variation

In order to accelerate object evaluation, some measurement systems commonly use an ordinal scale (e.g., stick results, quality estimation). This paper presents a way to analyze ordinal data variation. As in classical ANOVA for continual data, ORDANOVA for ordinal data splits the total variation into within and between components. This decomposition has various practical applications such as classification, cluster analysis, distinguishing feature identification and so on.     

Approximate queue length distribution of a discriminatory processor sharing queue with impatient customers

We consider a two-class processor sharing queueing system with impatient customers. The system operates under the discriminatory processor sharing (DPS) scheduling. The arrival process of each class customers is the Poisson process and the service requirement of a customer is exponentially distributed. The reneging rate of a customer is a constant. To analyze the performance of the system, we develop a time scale decomposition approach to approximate the joint queue-length distribution of each class customers. Via a numerical experiment, we show that the time scale decomposition approach gives a fairly good approximation of the queue-length distribution and the expected queue length.     

Combining Experts: Decomposition and Aggregation Order

In this article we ask, if quantities in an elicitation have been decomposed, is it better to combine experts before or after recomposing the quantities? We find that combining experts earlier, before recomposition of the quantities, leads to smaller errors with less variance. A simulation shows that these differences may be quite small on average; while an application to actual data shows that the differences can be significant in individual decision problems.