Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines

Abstract.  We consider marginal semiparametric partially linear models for longitudinal/clustered data and propose an estimation procedure based on a spline approximation of the non-parametric part of the model and an extension of the parametric marginal generalized estimating equations (GEE). Our estimates of both parametric part and non-parametric part of the model have properties parallel to those of parametric GEE, that is, the estimates are efficient if the covariance structure is correctly specified and they are still consistent and asymptotically normal even if the covariance structure is misspecified. By showing that our estimate achieves the semiparametric information bound, we actually establish the efficiency of estimating the parametric part of the model in a stronger sense than what is typically considered for GEE. The semiparametric efficiency of our estimate is obtained by assuming only conditional moment restrictions instead of the strict multivariate Gaussian error assumption.     

环境规制能否有效驱动高质量发展？——基于人力资本视角的理论与经验分析

在加强生态文明建设和扩大就业的背景下,环境规制能否同时实现环境保护、绿色就业与高质量发展等多重目标已成为亟待解决的重大问题。构建一种操作便捷的高质量发展评价指标,将其分解为结构效应、技术效应及规制效应,在统一框架内剖析环境规制影响高质量发展的人力资本机制,并使用联立方程空间自回归模型和省际面板数据进行检验,探究在各类人力资本因素调节下环境规制对高质量发展的非线性效应。研究发现：（1）环境规制能通过人力资本积累、产业结构升级、节能减排技术创新等途径影响高质量发展。（2）环境规制通过与人力资本溢价的动态匹配,能进一步推动产业结构升级和节能减排技术创新,助益高质量发展。（3）环境规制在人力资本因素调节下对高质量发展存在非线性影响。总体而言,人力资本因素的改善有利于充分发挥环境规制对高质量发展的倒逼效应;提升人力资本质量是当前调控人力资本因素、释放环境规制高质量发展效应的政策重点。（4）中国高质量发展存在显著为正的空间溢出效应,地方政府在环境问题中缺乏协同治理,削弱了这种空间溢出效应,因此全局层面的高质量发展有较大提升空间。充分激发环境规制的人力资本积累效应,从单纯注重人力资本“量”的扩张转向“质”的提升,实现区域协同治理,这对有效改善环境规制的高质量发展效应至关重要。     

Markov (Set) chains application to predict mortality rates using extended Milevsky–Promislov generalized mortality models

The mortality rates ( μx,t) measure the frequency of deaths in a fixed: population and time interval. The ability to model and forecast μx,t allows determining, among others, fundamental characteristics of life expectancy tables, e.g. used to determine the amount of premium in life insurance, adequate to the risk of death. The article proposes a new method of modelling and forecasting μx,t, using the class of stochastic Milevsky–Promislov switch models with excitations. The excitations are modelled by second, fourth and sixth order polynomials of outputs from the non-Gaussian Linear Scalar Filter (nGLSF) model and taking into account the Markov (Set) chain. The Markov (Set) chain state space is defined based on even orders of the nGLSF polynomial. The model order determines the theoretical values of the death rates. The obtained results usually provide a more precise forecast of the mortality rates than the commonly used Lee–Carter model.     

A robust approach to longitudinal data analysis

The author introduces robust techniques for estimation, inference and variable selection in the analysis of longitudinal data. She first addresses the problem of the robust estimation of the regression and nuisance parameters, for which she derives the asymptotic distribution. She uses weighted estimating equations to build robust quasi‐likelihood functions. These functions are then used to construct a class of test statistics for variable selection. She derives the limiting distribution of these tests and shows its robustness properties in terms of stability of the asymptotic level and power under contamination. An application to a real data set allows her to illustrate the benefits of a robust analysis.     

Regression Estimation Using Multivariate Failure Time Data and a Common Baseline Hazard Function Model

Recent ‘marginal’ methods for the regression analysis of multivariate failure time data have mostly assumed Cox (1972)model hazard functions in which the members of the cluster have distinct baseline hazard functions. In some important applications, including sibling family studies in genetic epidemiology and group randomized intervention trials, a common baseline hazard assumption is more natural. Here we consider a weighted partial likelihood score equation for the estimation of regression parameters under a common baseline hazard model, and provide corresponding asymptotic distribution theory. An extensive series of simulation studies is used to examine the adequacy of the asymptotic distributional approximations, and especially the efficiency gain due to weighting, as a function of strength of dependency within cluster, and cluster size. This revised version was published online in July 2006 with corrections to the Cover Date.     

核子中价夸克极化分布函数的OCD标度破坏

本文通过对A-P方程作Mellin变换和对演化函数的Mellin变换结果作展开近似,求得了核子中价夸克极化分布函数随Q~2变化的解析表达式,并利用所得结果给出了核子中夸克自旋不对称量的一些理论预言     

Estimating stellar-oscillation-related parameters and their uncertainties with the moment method

Summary.  The moment method is a well-known astronomical mode identification technique in asteroseismology which uses a time series of the first three moments of a spectral line to estimate the discrete oscillation mode parameters l and m . The method, in contrast with many other mode identification techniques, also provides estimates of other important continuous parameters such as the inclination angle α and the rotational velocity v _e. We developed a statistical formalism for the moment method based on so-called generalized estimating equations. This formalism allows an estimation of the uncertainty of the continuous parameters, taking into account that the different moments of a line profile are correlated and that the uncertainty of the observed moments also depends on the model parameters. Furthermore, we set up a procedure to take into account the mode uncertainty, i.e. the fact that often several modes ( l ,  m ) can adequately describe the data. We also introduce a new lack-of-fit function which works at least as well as a previous discriminant function, and which in addition allows us to identify the sign of the azimuthal order m . We applied our method to star HD181558 by using several numerical methods, from which we learned that numerically solving the estimating equations is an intensive task. We report on the numerical results, from which we gain insight in the statistical uncertainties of the physical parameters that are involved in the moment method.     

Multiple imputation compared with restricted pseudo‐likelihood and generalized estimating equations for analysis of binary repeated measures in clinical studies

Non‐likelihood‐based methods for repeated measures analysis of binary data in clinical trials can result in biased estimates of treatment effects and associated standard errors when the dropout process is not completely at random. We tested the utility of a multiple imputation approach in reducing these biases. Simulations were used to compare performance of multiple imputation with generalized estimating equations and restricted pseudo‐likelihood in five representative clinical trial profiles for estimating (a) overall treatment effects and (b) treatment differences at the last scheduled visit. In clinical trials with moderate to high (40–60%) dropout rates with dropouts missing at random, multiple imputation led to less biased and more precise estimates of treatment differences for binary outcomes based on underlying continuous scores. Copyright © 2005 John Wiley & Sons, Ltd.     

广义集压缩映射原理及其对积分方程组的应用

本文对Banach空间中映射组证明了一个不动点定理.利用这个定理,我们给出了Banach空间中非线性Fredholm和Volterra积分方程组解的存在性定理,也获得了非线性Volterra积分方程组极值解的存在定理和比较定理.这些定理推广了文[1]中的相应结果.     

一类非线性退缩抛物方程解的唯一性

本文研究下述Cauchy问题（其中）广义解的唯一性问题，在一定条件下，得到了唯一性结论，并给出严格证明．