Model Selection Criterion Based on the Multivariate Quasi‐Likelihood for Generalized Estimating Equations

The generalized estimating equations (GEE) approach has attracted considerable interest for the analysis of correlated response data. This paper considers the model selection criterion based on the multivariate quasi‐likelihood (MQL) in the GEE framework. The GEE approach is closely related to the MQL. We derive a necessary and sufficient condition for the uniqueness of the risk function based on the MQL by using properties of differential geometry. Furthermore, we establish a formal derivation of model selection criterion as an asymptotically unbiased estimator of the prediction risk under this condition, and we explicitly take into account the effect of estimating the correlation matrix used in the GEE procedure.     

A Class of Weighted Estimating Equations for Semiparametric Transformation Models with Missing Covariates

In survival analysis, covariate measurements often contain missing observations; ignoring this feature can lead to invalid inference. We propose a class of weighted estimating equations for right‐censored data with missing covariates under semiparametric transformation models. Time‐specific and subject‐specific weights are accommodated in the formulation of the weighted estimating equations. We establish unified results for estimating missingness probabilities that cover both parametric and non‐parametric modelling schemes. To improve estimation efficiency, the weighted estimating equations are augmented by a new set of unbiased estimating equations. The resultant estimator has the so‐called ‘double robustness’ property and is optimal within a class of consistent estimators.     

General purpose multiply robust data integration procedures for handling nonprobability samples

In recent years, there has been an increased interest in combining probability and nonprobability samples. Nonprobability sample are cheaper and quicker to conduct but the resulting estimators are vulnerable to bias as the participation probabilities are unknown. To adjust for the potential bias, estimation procedures based on parametric or nonparametric models have been discussed in the literature. However, the validity of the resulting estimators relies heavily on the validity of the underlying models. Also, nonparametric approaches may suffer from the curse of dimensionality and poor efficiency. We propose a data integration approach by combining multiple outcome regression models and propensity score models. The proposed approach can be used for estimating general parameters including totals, means, distribution functions, and percentiles. The resulting estimators are multiply robust in the sense that they remain consistent if all but one model are misspecified. The asymptotic properties of point and variance estimators are established. The results from a simulation study show the benefits of the proposed method in terms of bias and efficiency. Finally, we apply the proposed method using data from the Korea National Health and Nutrition Examination Survey and data from the National Health Insurance Sharing Services.     

二阶常微分方程组边值问题正解的存在性

利用锥上不动点定理,研究了一类二阶非线性常微分方程组四点边值问题正解的存在性.在非线性项满足一定增长的条件下,得到了至少一个和两个正解存在的几个充分条件.     

Continuous-time threshold autoregressions with jumps: Properties,estimation, and application to electricity markets

Continuous-time autoregressive processes have been applied successfully in many fields and are particularly advantageous in the modeling of irregularly spaced or high-frequency time series data. A convenient nonlinear extension of this model are continuous-time threshold autoregressions (CTAR). CTAR allow for greater flexibility in model parameters and can represent a regime switching behavior. However, so far only Gaussian CTAR processes have been defined, so that this model class could not be used for data with jumps, as frequently observed in financial applications. Hence, as a novelty, we construct CTAR processes with jumps in this paper. Existence of a unique weak solution and weak consistency of an Euler approximation scheme is proven. As a closed form expression of the likelihood is not available, we use kernel-based particle filtering for estimation. We fit our model to the Physical Electricity Index and show that it describes the data better than other comparable approaches.     

信息基础设施与经济增长——基于中国省际数据分析

利用2001年至2008年中国31个省、直辖市和自治区的面板数据验证信息基础设施对中国经济增长的影响,并在此基础上分析信息基础设施对中国不同区域经济增长贡献的大小.基于宏观总产出方程与信息基础设施微观供需模型相结合的联立方程模型控制信息基础设施内生性,采用人均长途光缆线路长度作为信息基础设施的代理变量测度信息基础设施对经济增长的贡献.实证研究结果表明,信息基础设施对中国的经济增长有显著的正向促进作用,基于信息基础设施对各地区经济增长的复合增长效应的测算表明,信息基础设施对中国经济增长有很大贡献,但是信息基础设施对不同区域增长的贡献与经济增长的状况却存在反差.在西部不发达地区,信息基础设施的发展对经济增长的促进作用要高于全国水平,而中部各省信息基础设施的发展却低于全国水平.     

Accuracy of Numerical Solutions Using the Euler Equation Residuals

This paper is concerned with asymptotic properties on the accuracy of numerical solutions. It is shown that the approximation error of the policy function is of the same order of magnitude as the size of the Euler equation residuals. Moreover, for bounding this approximation error the most relevant parameters are the discount factor and the curvature of the return function. These findings provide theoretical foundations for the construction of tests to assess the performance of alternative computational methods.     

Nonparametric Estimation of Triangular Simultaneous Equations Models

This paper presents a simple two-step nonparametric estimator for a triangular simultaneous equation model. Our approach employs series approximations that exploit the additive structure of the model. The first step comprises the nonparametric estimation of the reduced form and the corresponding residuals. The second step is the estimation of the primary equation via nonparametric regression with the reduced form residuals included as a regressor. We derive consistency and asymptotic normality results for our estimator, including optimal convergence rates. Finally we present an empirical example, based on the relationship between the hourly wage rate and annual hours worked, which illustrates the utility of our approach.     

Bayesian Inference for Hospital Quality in a Selection Model

This paper develops new econometric methods to infer hospital quality in a model with discrete dependent variables and nonrandom selection. Mortality rates in patient discharge records are widely used to infer hospital quality. However, hospital admission is not random and some hospitals may attract patients with greater unobserved severity of illness than others. In this situation the assumption of random admission leads to spurious inference about hospital quality. This study controls for hospital selection using a model in which distance between the patient's residence and alternative hospitals are key exogenous variables. Bayesian inference in this model is feasible using a Markov chain Monte Carlo posterior simulator, and attaches posterior probabilities to quality comparisons between individual hospitals and groups of hospitals. The study uses data on 74,848 Medicare patients admitted to 114 hospitals in Los Angeles County from 1989 through 1992 with a diagnosis of pneumonia. It finds the smallest and largest hospitals to be of the highest quality. There is strong evidence of dependence between the unobserved severity of illness and the assignment of patients to hospitals, whereby patients with a high unobserved severity of illness are disproportionately admitted to high quality hospitals. Consequently a conventional probit model leads to inferences about quality that are markedly different from those in this study's selection model.