Estimated estimating equations: semiparametric inference for clustered and longitudinal data

Summary.  We introduce a flexible marginal modelling approach for statistical inference for clustered and longitudinal data under minimal assumptions. This estimated estimating equations approach is semiparametric and the proposed models are fitted by quasi-likelihood regression, where the unknown marginal means are a function of the fixed effects linear predictor with unknown smooth link, and variance–covariance is an unknown smooth function of the marginal means. We propose to estimate the nonparametric link and variance–covariance functions via smoothing methods, whereas the regression parameters are obtained via the estimated estimating equations. These are score equations that contain nonparametric function estimates. The proposed estimated estimating equations approach is motivated by its flexibility and easy implementation. Moreover, if data follow a generalized linear mixed model, with either a specified or an unspecified distribution of random effects and link function, the model proposed emerges as the corresponding marginal (population-average) version and can be used to obtain inference for the fixed effects in the underlying generalized linear mixed model, without the need to specify any other components of this generalized linear mixed model. Among marginal models, the estimated estimating equations approach provides a flexible alternative to modelling with generalized estimating equations. Applications of estimated estimating equations include diagnostics and link selection. The asymptotic distribution of the proposed estimators for the model parameters is derived, enabling statistical inference. Practical illustrations include Poisson modelling of repeated epileptic seizure counts and simulations for clustered binomial responses.     

基于2007年投入产出表的我国投资乘数测算和变动分析

 本文对固定资产投资乘数、凯恩斯投资乘数和投入产出投资乘数等三种投资乘数进行了测算分析,结果表明近年来我国投资乘数并没有发生大幅度下降,对经济增长的拉动贡献较大。通过对4万亿投资计划的具体测算,表明投资对拉动内需和抵御外部冲击发挥了巨大作用。作为发展中国家,保持较高的投资增速是经济可持续发展的必要条件,未来投资仍将是拉动我国经济增长的主要动力。但应当积极调整投资结构,避免产能过剩、抑制房地产价格上涨,提高投资效率。     

Identification of Salmonella high risk pig-herds in Belgium by using semiparametric quantile regression

Summary.  Consumption of pork that is contaminated with Salmonella is an important source of human salmonellosis world wide. To control and prevent salmonellosis, Belgian pig-herds with high Salmonella infection burden are encouraged to take part in a control programme supporting the implementation of control measures. The Belgian government decided that only the 10% of pig-herds with the highest Salmonella infection burden (denoted high risk herds) can participate. To identify these herds, serological data reported as sample-to-positive ratios (SP-ratios) are collected. However, SP-ratios have an extremely skewed distribution and are heavily subject to confounding seasonal and animal age effects. Therefore, we propose to identify the 10% high risk herds by using semiparametric quantile regression with P -splines. In particular, quantile curves of animal SP-ratios are estimated as a function of sampling time and animal age. Then, pigs are classified into low and high risk animals with high risk animals having an SP-ratio that is larger than the corresponding estimated upper quantile. Finally, for each herd, the number of high risk animals is calculated as well as the beta–binomial p -value reflecting the hypothesis that the Salmonella infection burden is higher in that herd compared with the other herds. The 10% pig-herds with the lowest p -values are then identified as high risk herds. In addition, since high risk herds are supported to implement control measures, a risk factor analysis is conducted by using binomial generalized linear mixed models to investigate factors that are associated with decreased or increased Salmonella infection burden. Finally, since the choice of a specific upper quantile is to a certain extent arbitrary, a sensitivity analysis is conducted comparing different choices of upper quantiles.     

基于SYS-GMM的中国人口结构变化与经济增长关系研究

本文利用中国29个省份20年的面板数据,探讨了人口结构变化对储蓄、投资和经济增长的影响。我们将人口结构指标引入传统的经济增长模型中,并用固定效应模型和SYS-GMM计量方法分别测算其对储蓄、投资和经济增长的效应。考虑到老年抚养比在经济增长方程的内生性,我们还将滞后30年的就业人数比率作为工具变量来识别老年抚养比对经济增长的因果效应。结果显示老年抚养率对储蓄、投资和经济增长存在显著的正相关。人口增长率对储蓄和投资有着负相关,但对经济增长没有影响。工作年龄人口比率对储蓄率存在负相关,对投资和经济增长存在正向影响但估计的回归系数不显著。在加入其它制度和人口变量之后回归结果依然稳定。     

Optimal investment and premium control for insurers with ambiguity

Abstract

In this paper, we consider the optimal investment and premium control problem for insurers who worry about model ambiguity. Different from previous works, we assume that the insurer’s surplus process is described by a non-homogeneous compound Poisson model and the insurer has ambiguity on both the financial market and the insurance market. Our purpose is to find the impacts of model ambiguity on optimal policies. With the objective of maximizing the expected utility of terminal wealth, the closed-form solutions of the optimal investment and premium policies are obtained by solving HJB equations. Finally, numerical examples are also given to illustrate the results.     

住宅价格与土地价格的城市差异及其决定因素

本文通过建立中国城市住宅市场与土地市场的联立方程模型,试图解释住宅价格、土地价格的城市间差异。通过收集中国35个大中城市的105个样本数据,利用OLS和2SLS两种方法估计了城市住宅价格与土地价格方程。实证结果表明住宅市场与土地市场是互动影响的关联资产市场,住宅价格与土地价格之间存在联立性。人口数量、财富水平、建筑成本、住宅预期收益和土地市场化程度是造成中国城市间住宅价格、土地价格差异的决定因素,而平均工资与城市宜人性的影响并不显著。     

Mixed-Poisson Point Process with Partially-Observed Covariates: Ecological Momentary Assessment of Smoking

Ecological Momentary Assessment is an emerging method of data collection in behavioral research that may be used to capture the times of repeated behavioral events on electronic devices, and information on subjects' psychological states through the electronic administration of questionnaires at times selected from a probability-based design as well as the event times. A method for fitting a mixed Poisson point process model is proposed for the impact of partially-observed, time-varying covariates on the timing of repeated behavioral events. A random frailty is included in the point-process intensity to describe variation among subjects in baseline rates of event occurrence. Covariate coefficients are estimated using estimating equations constructed by replacing the integrated intensity in the Poisson score equations with a design-unbiased estimator. An estimator is also proposed for the variance of the random frailties. Our estimators are robust in the sense that no model assumptions are made regarding the distribution of the time-varying covariates or the distribution of the random effects. However, subject effects are estimated under gamma frailties using an approximate hierarchical likelihood. The proposed approach is illustrated using smoking data.     

Deletion diagnostics for marginal mean and correlation model parameters in estimating equations

Regression diagnostics are introduced for parameters in marginal association models for clustered binary outcomes in an implementation of generalized estimating equations. Estimating equations for intracluster correlations facilitate computational formulae for one-step deletion diagnostics in an extension of earlier work on diagnostics for parameters in the marginal mean model. The proposed diagnostics measure the influence of an observation or a cluster of observations on the estimated regression parameters and on the overall fit of the model. The diagnostics are applied to data from four research studies from public health and medicine.     

Data analysis of sales of natural gas to households in the United States

Regression diagnostics and a time series analysis of residuals are used to help define regression equations and to identify, the weaknesses of these equations for explaining monthly deliveries of natural gas to residential customers in the United States for the time period April 1979 through March 1983. More than 99% of the monthly variation in deliveries is explained by a linear regression equation which includes heating degree days, cooling degree days, and the price of natural gas as independent variables. Final estimated relationships yield useful monthly and annual estimates of natural gas deliveries to residential customers in the United States for the time period April 1983 through March 1984. Most importantly, the estimated results when used in conjunction with the diagnostics and the time series analysis of the residuals indicate the possible strengths, weaknesses, and applicability of the estimated relationships.     

中国经济增长的就业弹性

 本文利用2001-2008年中国深沪两市508家制造业上市公司的微观就业数据和企业动态劳动需求方程来重新估计了中国经济增长的就业弹性。实证结果表明,中国制造业上市公司的总资产规模扩张（即企业投资）具有显著的就业效应。因此,企业微观数据并不支持中国经济增长的就业弹性下降或偏低的观点。     

Functional quasi-likelihood regression models with smooth random effects

Summary. We propose a class of semiparametric functional regression models to describe the influence of vector-valued covariates on a sample of response curves. Each observed curve is viewed as the realization of a random process, composed of an overall mean function and random components. The finite dimensional covariates influence the random components of the eigenfunction expansion through single-index models that include unknown smooth link and variance functions. The parametric components of the single-index models are estimated via quasi-score estimating equations with link and variance functions being estimated nonparametrically. We obtain several basic asymptotic results. The functional regression models proposed are illustrated with the analysis of a data set consisting of egg laying curves for 1000 female Mediterranean fruit-flies (medflies).     

Estimable functions in the nonlinear model

When the method of least squares is used to estimate the parameters in a general model and the generated system of normal equations is linearly dependent, the estimate of the vector of parameters which satisfies the criterion is not unique. However, there exist certain functions of the estimated vector of parameters which are invariant to the least squares solution obtained from the normal equations. We define those invariant functions to be estimable, and present a technique to determine the functions of the parameters which are estimable for the general model. The method results in solving either a linear first order partial differential equation or a system of linear first order partial differential equations corresponding, respectively, to a single or multiple dependency between columns of the Jacobian matrix of the mean of the model. The usual results concerning estimability for linear models are a special case of the general results developed.     

A Multivariate Intervention Model for the Dutch Mint Circulation: Estimation and Monte Carlo Simulation

For each of the five Dutch coinage denominations, a transfer-function model is estimated. The output variables are monthly observations of coins in circulation. Two input variables represent transaction flows; all other inputs are step functions, representing the occurrence of interventions. Using the method of cross-correlating the residuals of the individual equations, a multivariate transfer-function model is constructed and estimated. Next Monte Carlo simulation is applied to derive expectations and variances of the yearly addition to the stock of coins until 1996. Our results enlighten on some aspects of a problem situation faced by the Dutch State Mint.     

Expected estimating equations to accommodate covariate measurement error

Estimating equations which are not necessarily likelihood-based score equations are becoming increasingly popular for estimating regression model parameters. This paper is concerned with estimation based on general estimating equations when true covariate data are missing for all the study subjects, but surrogate or mismeasured covariates are available instead. The method is motivated by the covariate measurement error problem in marginal or partly conditional regression of longitudinal data. We propose to base estimation on the expectation of the complete data estimating equation conditioned on available data. The regression parameters and other nuisance parameters are estimated simultaneously by solving the resulting estimating equations. The expected estimating equation (EEE) estimator is equal to the maximum likelihood estimator if the complete data scores are likelihood scores and conditioning is with respect to all the available data. A pseudo-EEE estimator, which requires less computation, is also investigated. Asymptotic distribution theory is derived. Small sample simulations are conducted when the error process is an order 1 autoregressive model. Regression calibration is extended to this setting and compared with the EEE approach. We demonstrate the methods on data from a longitudinal study of the relationship between childhood growth and adult obesity.     

Fast approximate Bayesian computation for estimating parameters in differential equations

Approximate Bayesian computation (ABC) using a sequential Monte Carlo method provides a comprehensive platform for parameter estimation, model selection and sensitivity analysis in differential equations. However, this method, like other Monte Carlo methods, incurs a significant computational cost as it requires explicit numerical integration of differential equations to carry out inference. In this paper we propose a novel method for circumventing the requirement of explicit integration by using derivatives of Gaussian processes to smooth the observations from which parameters are estimated. We evaluate our methods using synthetic data generated from model biological systems described by ordinary and delay differential equations. Upon comparing the performance of our method to existing ABC techniques, we demonstrate that it produces comparably reliable parameter estimates at a significantly reduced execution time.     

Prediction under uncertainty of degree of polynomial in growth curve models

Random coefficient polynomial regression model has been considered for prediction purpose when there is uncertainty about the degree of the polynomialo Expressions for mean square errors of two predictors based on simple estimators have been derived and their perfomaiices have been compared when parameters are estimated from the sample. A modified predictor has also been suggested when parameters in the predicting equations are to be estimated from the sample. Perform-ance ofseveral predictors haife been compared by cross validation technique from a real set of data.     

基于贝叶斯面板模型的扩展C-D生产函数估计及实证

利用2008—2011年的省际面板数据并充分收集和整理先验信息,运用贝叶斯面板模型分析和研究了扩展的C-D生产函数,有效地处理了短期时序造成的小样本问题以及误差项之间的相关性问题,实现参数的适时修正和更新。研究发现:目前中国物质资本份额的后验均值为55%,明显低于中国学者估计的60%;人力资本所占份额仅为5%~6%,其对经济增长的拉动作用没有得到充分的发挥,中国应增大人力资本投入;固定资产投资比例人均产出弹性的后验均值为1.37;地理位置等个体差异依旧是造成中国发展不平衡问题逐年扩大的重要原因。     

Comparing volatility forecasting models during the global financial crisis

Volatility estimation in financial markets has always been a challenge especially in time of crisis. Once asset prices and investment decisions are highly sensitive to such variable, many different models have been proposed in literature. This article estimates the volatility from a new family of stochastic volatility models called non-Gaussian State Space Models, a subclass of state space models where it is possible to compute exact likelihood. Volatilities of important Asian and Oceanian stock market indexes have been estimated and compared to APARCH model estimates. Results showed that non-Gaussian State Space Models outperformed significantly in both in-sample and forecasting cases.     

Conditional versus unconditional analysis in some regression models

This paper discusses extensions of the variability of the parameters (or functions of parameters) in a recursive system of regression models, and shows that conditioning on the carriers may lead to drastically different conclusions than when the carriers are viewed as stochastic. The relationships among the variables in these models are derived by a sequence of regressions, in which the dependent variable of one equation may reappear as a carrier in a later equation. The model to be fitted need not be identical with the generating equations. In these recursive systems of equations, when the models are miss-specified, or when functions of parameters from different equations are to be estimated, the variability of the estimators is shown to depend critically on the level of conditioning assumed. Various jackknife and bootstrap methods of estimating the variability of the estimators are suggested. In particular the bootstrap estimators of variability can be adopted to captured the correct level of conditioning, by mimicking the conditioning in their design. Two problems in which the level of conditioning matters are described and analysed under the general chained regression models. A real data problem. Omission of variables is sometimes advocated for reducting the variance of the remaining estimators. In both cases the effectiveness of the nonparametric variance estimators is demonstrated using simulation studies.     

Statistical inference for some Volterra population processes in a random environment

We study the problem of maximum-likelihood estimation in some random-environment population models, defined through nonlinear ltǒ stochastic differential equations. It is shown that a criticality parameter can be estimated consistently. The asymptotic behavior of the estimators is analyzed, and a goodness-of-fit test is proposed.