Quantitative Analysis on the Impact of Urbanisation on Chinese Population Aging

This paper systematically studies the impact of fertility, mortality, initial age structure and rural-urban migration on population aging in rural and urban China from 2000 to 2010. The results show that urbanisation plays a crucial role in population aging in both rural and urban areas and its inf luence is closely linked to the age pattern of the migrants. One third of young rural population transformed into urban population during that period. The contribution of rural-urban migration to population aging in rural areas is 43.4 percent, which is higher than any inf luences from population’s natural changes, and is dominant in population aging in the countryside. Rural-urban migration contributes-118.0 percent to population aging in urban areas by reducing the proportion of aged population and its influence was only lower than that of the initial age structure. The impact of urbanisation on population aging in towns is relatively limited. Among factors from population’s natural changes, the inf luence of the initial age structure is higher than those from changes of mortality and fertility. The paper discusses the causes and developmental trends of impact of urbanisation on population aging between rural and urban areas, and addresses some policy recommendations to deal with socio-economic challenges.     

浅谈学分制及其实施中存在的问题与对策

我国高校正在实施学分制管理制度改革,本文阐述学分制的特征、学分制的优缺点,分析目前高校学分制实施中存在的问题及其相应的对策.     

Maximum Likelihood Estimations and EM Algorithms with Length-biased Data

Length-biased sampling has been well recognized in economics, industrial reliability, etiology applications, epidemiological, genetic and cancer screening studies. Length-biased right-censored data have a unique data structure different from traditional survival data. The nonparametric and semiparametric estimations and inference methods for traditional survival data are not directly applicable for length-biased right-censored data. We propose new expectation-maximization algorithms for estimations based on full likelihoods involving infinite dimensional parameters under three settings for length-biased data: estimating nonparametric distribution function, estimating nonparametric hazard function under an increasing failure rate constraint, and jointly estimating baseline hazards function and the covariate coefficients under the Cox proportional hazards model. Extensive empirical simulation studies show that the maximum likelihood estimators perform well with moderate sample sizes and lead to more efficient estimators compared to the estimating equation approaches. The proposed estimates are also more robust to various right-censoring mechanisms. We prove the strong consistency properties of the estimators, and establish the asymptotic normality of the semi-parametric maximum likelihood estimators under the Cox model using modern empirical processes theory. We apply the proposed methods to a prevalent cohort medical study. Supplemental materials are available online.     

SPECIAL ISSUE： REGIONAL CONVERGENCE AND COORDINATED URBAN GROWTH Spatial Spillovers and the Convergence of Regional Economic Growth： A Case Study Based on the Yangtze River Delta

空间俱乐部趋同是指经济增长初始条件和结构特征相似且空间上相邻的一组区域的经济增长收敛于相同的稳态,是区域经济增长俱乐部趋同的一个新研究领域,其发生机制是空间外溢促成区域经济出现地方化增长,进而导致空间俱乐部趋同。运用包含空间外溢的区域经济增长理论模型可以证明,空间外溢有可能导致空间俱乐部趋同。对中国长江三角洲1990--2007年区域经济增长过程所做的经验分析也表明,空间外溢对区域经济增长确有影响,空间俱乐部趋同客观存在。在考虑空间外溢的情况下,长江三角洲的空间俱乐部趋同速度为1．57％。     

A Partially Linear Regression Model for Data from an Outcome-Dependent Sampling Design

The outcome dependent sampling scheme has been gaining attention in both the statistical literature and applied fields. Epidemiological and environmental researchers have been using it to select the observations for more powerful and cost-effective studies. Motivated by a study of the effect of in utero exposure to polychlorinated biphenyls on children's IQ at age 7, in which the effect of an important confounding variable is nonlinear, we consider a semi-parametric regression model for data from an outcome-dependent sampling scheme where the relationship between the response and covariates is only partially parameterized. We propose a penalized spline maximum likelihood estimation (PSMLE) for inference on both the parametric and the nonparametric components and develop their asymptotic properties. Through simulation studies and an analysis of the IQ study, we compare the proposed estimator with several competing estimators. Practical considerations of implementing those estimators are discussed.     

波利亚数学发现观与数学教学改革

本文论述了波利亚数学发现观，探讨了它的内容和特点，提出了若干改进数学教学的意见．     

Analyzing Length-biased Data with Semiparametric Transformation and Accelerated Failure Time Models

Right-censored time-to-event data are often observed from a cohort of prevalent cases that are subject to length-biased sampling. Informative right censoring of data from the prevalent cohort within the population often makes it difficult to model risk factors on the unbiased failure times for the general population, because the observed failure times are length biased. In this paper, we consider two classes of flexible semiparametric models: the transformation models and the accelerated failure time models, to assess covariate effects on the population failure times by modeling the length-biased times. We develop unbiased estimating equation approaches to obtain the consistent estimators of the regression coefficients. Large sample properties for the estimators are derived. The methods are confirmed through simulations and illustrated by application to data from a study of a prevalent cohort of dementia patients.     

Imputation for semiparametric transformation models with biased-sampling data

Widely recognized in many fields including economics, engineering, epidemiology, health sciences, technology and wildlife management, length-biased sampling generates biased and right-censored data but often provide the best information available for statistical inference. Different from traditional right-censored data, length-biased data have unique aspects resulting from their sampling procedures. We exploit these unique aspects and propose a general imputation-based estimation method for analyzing length-biased data under a class of flexible semiparametric transformation models. We present new computational algorithms that can jointly estimate the regression coefficients and the baseline function semiparametrically. The imputation-based method under the transformation model provides an unbiased estimator regardless whether the censoring is independent or not on the covariates. We establish large-sample properties using the empirical processes method. Simulation studies show that under small to moderate sample sizes, the proposed procedure has smaller mean square errors than two existing estimation procedures. Finally, we demonstrate the estimation procedure by a real data example.     

Nonparametric tests for right-censored data with biased sampling

Testing the equality of two survival distributions can be difficult in a prevalent cohort study when non random sampling of subjects is involved. Due to the biased sampling scheme, independent censoring assumption is often violated. Although the issues about biased inference caused by length-biased sampling have been widely recognized in statistical, epidemiological and economical literature, there is no satisfactory solution for efficient two-sample testing. We propose an asymptotic most efficient nonparametric test by properly adjusting for length-biased sampling. The test statistic is derived from a full likelihood function, and can be generalized from the two-sample test to a k-sample test. The asymptotic properties of the test statistic under the null hypothesis are derived using its asymptotic independent and identically distributed representation. We conduct extensive Monte Carlo simulations to evaluate the performance of the proposed test statistics and compare them with the conditional test and the standard logrank test for different biased sampling schemes and right-censoring mechanisms. For length-biased data, empirical studies demonstrated that the proposed test is substantially more powerful than the existing methods. For general left-truncated data, the proposed test is robust, still maintains accurate control of type I error rate, and is also more powerful than the existing methods, if the truncation patterns and right-censoring patterns are the same between the groups. We illustrate the methods using two real data examples.     

Dimension reduced kernel estimation for distribution function with incomplete data

This work focuses on the estimation of distribution functions with incomplete data, where the variable of interest Y has ignorable missingness but the covariate X is always observed. When X is high dimensional, parametric approaches to incorporate X—information is encumbered by the risk of model misspecification and nonparametric approaches by the curse of dimensionality. We propose a semiparametric approach, which is developed under a nonparametric kernel regression framework, but with a parametric working index to condense the high dimensional X—information for reduced dimension. This kernel dimension reduction estimator has double robustness to model misspecification and is most efficient if the working index adequately conveys the X—information about the distribution of Y. Numerical studies indicate better performance of the semiparametric estimator over its parametric and nonparametric counterparts. We apply the kernel dimension reduction estimation to an HIV study for the effect of antiretroviral therapy on HIV virologic suppression.