Adaptive robust estimation in joint mean–covariance regression model for bivariate longitudinal data

The estimation of the covariance matrix is important in the analysis of bivariate longitudinal data. A good estimator for the covariance matrix can improve the efficiency of the estimators of the mean regression coefficients. Furthermore, the covariance estimation itself is also of interest, but it is a challenging job to model the covariance matrix of bivariate longitudinal data due to the complex structure and positive definite constraint. In addition, most of existing approaches are based on the maximum likelihood, which is very sensitive to outliers or heavy-tail error distributions. In this article, an adaptive robust estimation method is proposed for bivariate longitudinal data. Unlike the existing likelihood-based methods, the proposed method can adapt to different error distributions. Specifically, at first, we utilize the modified Cholesky block decomposition to parameterize the covariance matrices. Secondly, we apply the bounded Huber's score function to develop a set of robust generalized estimating equations to estimate the parameters both in the mean and the covariance models simultaneously. A data-driven approach is presented to select the parameter c in the Huber's score function, which can ensure that the proposed method is robust and efficient. A simulation study and a real data analysis are conducted to illustrate the robustness and efficiency of the proposed approach.     

Two-stage Liu estimator in a simultaneous equations model

Two-stage least squares estimation in a simultaneous equations model has several desirable properties under the problem of multicollinearity. So, various kinds of improved estimation techniques can be developed to deal with the problem of multicollinearity. One of them is ridge regression estimation that can be applied at both stages and defined in Vinod and Ullah [Recent advances in regression methods. New York: Marcel Dekker; 1981]. We propose three different kinds of Liu estimators that are named by their implementation stages. Mean square errors are derived to compare the performances of the mentioned estimators and two different choices of the biasing parameter are offered. Moreover, a numerical example is given with a data analysis based on the Klein Model I and a Monte Carlo experiment is conducted.     

完全竞争市场的一般均衡计算——基于福利方程的分析框架

一般均衡理论是现代经济学最为重要的组成部分和分析方法,而一般均衡的计算则是进行经济分析的前提和基础。从理论上看,完全竞争市场的一般均衡的计算主要有超额需求方程组和福利方程组两种方法,前一种方法在文献和实践中论述较多,而后一种方法则鲜有文献涉及和应用。本文对基于福利方程组的计算方法的原理和计算步骤进行了归纳阐述,并在此基础上给出了具体例子来比较两种计算方法的优劣。     

Closed‐form likelihoods for stochastic differential equation growth models

The authors derive closed‐form expressions for the full, profile, conditional and modified profile likelihood functions for a class of random growth parameter models they develop as well as Garcia's additive model. These expressions facilitate the determination of parameter estimates for both types of models. The profile, conditional and modified profile likelihood functions are maximized over few parameters to yield a complete set of parameter estimates. In the development of their random growth parameter models the authors specify the drift and diffusion coefficients of the growth parameter process in a natural way which gives interpretive meaning to these coefficients while yielding highly tractable models. They fit several of their random growth parameter models and Garcia's additive model to stock market data, and discuss the results. The Canadian Journal of Statistics 38: 474–487; 2010 © 2010 Statistical Society of Canada     

Orthogonalized Residuals for Estimation of Marginally Specified Association Parameters in Multivariate Binary Data

Abstract. This paper focuses on marginal regression models for correlated binary responses when estimation of the association structure is of primary interest. A new estimating function approach based on orthogonalized residuals is proposed. A special case of the proposed procedure allows a new representation of the alternating logistic regressions method through marginal residuals. The connections between second‐order generalized estimating equations, alternating logistic regressions, pseudo‐likelihood and other methods are explored. Efficiency comparisons are presented, with emphasis on variable cluster size and on the role of higher‐order assumptions. The new method is illustrated with an analysis of data on impaired pulmonary function.     

Estimation of small area event rates and of the associated standard errors

We develop empirical best estimators for small area event rates based on the hierarchical Poisson model with log-normal mixing distribution, when the basic data consists of area level measurements. We derive an approximate expression to the mean squared error of the estimators and we provide a method for estimating this expression.     

具有变系数的2n阶中立型微分方程正解的存在性

本文给出具有变系数Ｐ（ｔ）的２ｎ阶中立型微分方程 （ｘ（ｔ）－Ｐ（ｔ）_ｘ（ｔ－τ））~（２ｎ）+ｆ（ｔ,ｘ（ｔ－τ_1（ｔ））,...,ｘ（ｔ－τ_ｍ（ｔ）））＝０正解存在的若干个充分条件．本文结果部分地回答了文［１］提出的问题．     

Endogenous Growth of Population and Income Depending on Resource and Knowledge

We consider a three sector demoeconomic model and its interdependence with the accumulation of human capital and resources. The primary sector harvests a renewable resource which constitutes the input into industrial production, the secondary sector of our economy. Both sectors are always affected by the stock of knowledge. The tertiary sector is responsible for the accumulation of this stock that represents a public good for all three sectors. Labour is divided up between the three sectors under the assumption of competitive labour markets. The economy exhibits two externalities—free access to renewable resource harvesting and the existence of a public stock of knowledge—that are not properly reflected in competitive markets. We internalize these externalities by taxing the output of the primary sector and use these taxes together with taxes on labour income to finance the inputs of the tertiary sector. The central focus of this study is whether and what kind of interactions between the economy, the population and the environment foster sustainability and if possible, continuous growth. The views expressed in this paper are the first author’s own views and do not necessarily represent those of the Max Planck Institute for Demographic Research.     

A comparison of population average and random-effect models for the analysis of longitudinal count data with base-line information

The generalized estimating equation (GEE) approach to the analysis of longitudinal data has many attractive robustness properties and can provide a 'population average' characterization of interest, for example, to clinicians who have to treat patients on the basis of their observed characteristics. However, these methods have limitations which restrict their usefulness in both the social and the medical sciences. This conclusion is based on the premise that the main motivations for longitudinal analysis are insight into microlevel dynamics and improved control for omitted or unmeasured variables. We claim that to address these issues a properly formulated random-effects model is required. In addition to a theoretical assessment of some of the issues, we illustrate this by reanalysing data on polyp counts. In this example, the covariates include a base-line outcome, and the effectiveness of the treatment seems to vary by base-line. We compare the random-effects approach with the GEE approach and conclude that the GEE approach is inappropriate for assessing the treatment effects for these data.     

不完全竞争条件下的双向决策模型

本文依据不完全竞争的特点,运用模糊关系方程及其解法,给出了厂商在垄断、寡头和垄断竞争市场中的综合决策模型。厂商可按该模型决策,改进产品的综合水平,提高经济效益。