On equality of ordinary least squares estimator,best linear unbiased estimator and best linear unbiased predictor in the general linear model

The equality of ordinary least squares estimator (OLSE), best linear unbiased estimator (BLUE) and best linear unbiased predictor (BLUP) in the general linear model with new observations is investigated through matrix rank method, some new necessary and sufficient conditions are given.     

长三角科技资源配置能力与城市化进程的协调耦合关系研究

科技资源配置能力已成为长江地区城市化进程的重要推力。因此,在构建科技资源与城市化耦合系统评价指标体系的基础上,利用耦合协调度模型综合评价长江区域科技资源配置与城市化的交互耦合关系。结果显示:从时间维度看,研究期内长三角科技资源配置能力与城市化进程之间的耦合关系基本上处于磨合阶段,耦合协调度以低度协调耦合状态为主并逐步过渡到中度协调耦合状态;从空间维度看,长三角各城市的科技资源配置与城市化耦合协调度在极度协调耦合、高度协调耦合、中度协调耦合、低度协调耦合四个阶段均有分布,层级分明且大部分城市尚处于低度协调耦合状态。     

收入分布函数在收入不平等研究领域的应用

收入分布函数的研究对于收入不平等的探讨意义重大,但是国内该领域的研究尚待进一步的拓展。笔者在文献回顾的基础上梳理了国外的相关研究,把常用的分布函数分成两参数分布和多参数分布函数两类,介绍了各类函数拟合居民实际收入分布的效果及其与基尼系数的关系;同时,本文剖析了各类函数之间的内在联系;进一步,基于分布函数的角度,笔者研究了收入流动性与收入不平等之间的联系,分析了平均数和中位数比值与基尼系数之间的数学关系以及如何利用该比值来估计分布函数的参数。利用这些研究结果,文章探讨了2010年我国城镇居民的收入结构和贫困问题并提出了一些前瞻性的研究建议。     

Asymptotic convergence of dimension reduction based boosting in classification

In high dimensional classification problem, two stage method, reducing the dimension of predictor first and then applying the classification method, is a natural solution and has been widely used in many fields. The consistency of the two stage method is an important issue, since errors induced by dimension reduction method inevitably have impacts on the following classification method. As an effective method for classification problem, boosting has been widely used in practice. In this paper, we study the consistency of two stage method–dimension reduction based boosting algorithm (briefly DRB) for classification problem. Theoretical results show that Lipschitz condition on the base learner is required to guarantee the consistency of DRB. This theoretical findings provide useful guideline for application.     

Estimation with right‐censored observations under a semi‐Markov model

The semi‐Markov process often provides a better framework than the classical Markov process for the analysis of events with multiple states. The purpose of this paper is twofold. First, we show that in the presence of right censoring, when the right end‐point of the support of the censoring time is strictly less than the right end‐point of the support of the semi‐Markov kernel, the transition probability of the semi‐Markov process is nonidentifiable, and the estimators proposed in the literature are inconsistent in general. We derive the set of all attainable values for the transition probability based on the censored data, and we propose a nonparametric inference procedure for the transition probability using this set. Second, the conventional approach to constructing confidence bands is not applicable for the semi‐Markov kernel and the sojourn time distribution. We propose new perturbation resampling methods to construct these confidence bands. Different weights and transformations are explored in the construction. We use simulation to examine our proposals and illustrate them with hospitalization data from a recent cancer survivor study. The Canadian Journal of Statistics 41: 237–256; 2013 © 2013 Statistical Society of Canada     

Parameter estimation of nonlinear mixed-effects models using first-order conditional linearization and the EM algorithm

Nonlinear mixed-effects (NLME) models are flexible enough to handle repeated-measures data from various disciplines. In this article, we propose both maximum-likelihood and restricted maximum-likelihood estimations of NLME models using first-order conditional expansion (FOCE) and the expectation–maximization (EM) algorithm. The FOCE-EM algorithm implemented in the ForStat procedure SNLME is compared with the Lindstrom and Bates (LB) algorithm implemented in both the SAS macro NLINMIX and the S-Plus/R function nlme in terms of computational efficiency and statistical properties. Two realworld data sets an orange tree data set and a Chinese fir (Cunninghamia lanceolata) data set, and a simulated data set were used for evaluation. FOCE-EM converged for all mixed models derived from the base model in the two realworld cases, while LB did not, especially for the models in which random effects are simultaneously considered in several parameters to account for between-subject variation. However, both algorithms had identical estimated parameters and fit statistics for the converged models. We therefore recommend using FOCE-EM in NLME models, particularly when convergence is a concern in model selection.     

Generalized varying-coefficient single-index model

In this paper, the generalized varying-coefficient single-index model is discussed based on penalized likelihood. All the unknown functions are fitted by penalized spline. The estimates of the unknown parameters and the unknown coefficient functions are obtained and the estimation approach is rapid and computationally stable. Under some mild conditions, the consistency and the asymptotic normality of these resulting estimators are given. Two simulation studies are carried out to illustrate the performance of the estimates. An application of the model to the Hong Kong environmental data further demonstrates the potential of the proposed modelling procedures.