Semiparametric maximum likelihood for measurement error model regression

This paper presents an EM algorithm for semiparametric likelihood analysis of linear, generalized linear, and nonlinear regression models with measurement errors in explanatory variables. A structural model is used in which probability distributions are specified for (a) the response and (b) the measurement error. A distribution is also assumed for the true explanatory variable but is left unspecified and is estimated by nonparametric maximum likelihood. For various types of extra information about the measurement error distribution, the proposed algorithm makes use of available routines that would be appropriate for likelihood analysis of (a) and (b) if the true x were available. Simulations suggest that the semiparametric maximum likelihood estimator retains a high degree of efficiency relative to the structural maximum likelihood estimator based on correct distributional assumptions and can outperform maximum likelihood based on an incorrect distributional assumption. The approach is illustrated on three examples with a variety of structures and types of extra information about the measurement error distribution.     

A dynamic analysis of air pollution emissions in China: Evidence from nonparametric additive regression models

PM_2.5 emissions not only have serious adverse health effects, but also impede transportation activities, especially in air and highway transport. As a result, PM_2.5 emissions have become a public policy concern in China in recent years. Currently, the vast majority of existing researches on PM_2.5 are based on natural science perspective. Very few economic studies on the subject have been conducted with linear models. This paper adopts provincial panel data from 2001 to 2012, and uses the STIRPAT model and nonparametric additive regression models to examine the key driving forces of PM_2.5 emissions in China. The results show that the nonlinear effect of economic growth on PM_2.5 emissions is consistent with the Environmental Kuznets Curve (EKC) hypothesis. The nonlinear impact of urbanization exhibits an inverted “U-shaped” pattern due to the rapid development of urban real estate in the early stages and the strengthening of environmental protection measures in the latter stage. Coal consumption follows an inverted “U-shaped” relationship with PM_2.5 emissions owing to massive coal consumption at the beginning and efforts to optimize the energy structure as well as technological progress in clean energy in the latter stages. The nonlinear inverted “U-shaped” impact of private vehicles may be due to the different roles of scale, structural and technical effects at different stages. However, energy efficiency improvement follows a positive “U-shaped” pattern in relation to PM_2.5 emissions because of differences in the scale of the economy and the speed of technological progress at different times. As a result, the differential dynamic effects of the driving forces of PM_2.5 emissions at different times should be taken into consideration when initiating policies to reduce PM_2.5 emissions in China.     

Polynomial spline estimation and inference of proportional hazards regression models with flexible relative risk form

The Cox proportional hazards model usually assumes an exponential form for the dependence of the hazard function on covariate variables. However, in practice this assumption may be violated and other relative risk forms may be more appropriate. In this article, we consider the proportional hazards model with an unknown relative risk form. Issues in model interpretation are addressed. We propose a method to estimate the relative risk form and the regression parameters simultaneously by first approximating the logarithm of the relative risk form by a spline, and then employing the maximum partial likelihood estimation. An iterative alternating optimization procedure is developed for efficient implementation. Statistical inference of the regression coefficients and of the relative risk form based on parametric asymptotic theory is discussed. The proposed methods are illustrated using simulation and an application to the Veteran's Administration lung cancer data.     

Gaussian process functional regression modeling for batch data

A Gaussian process functional regression model is proposed for the analysis of batch data. Covariance structure and mean structure are considered simultaneously, with the covariance structure modeled by a Gaussian process regression model and the mean structure modeled by a functional regression model. The model allows the inclusion of covariates in both the covariance structure and the mean structure. It models the nonlinear relationship between a functional output variable and a set of functional and nonfunctional covariates. Several applications and simulation studies are reported and show that the method provides very good results for curve fitting and prediction.     

Boosted regression trees with errors in variables

In this article, we consider nonparametric regression when covariates are measured with error. Estimation is performed using boosted regression trees, with the sum of the trees forming the estimate of the conditional expectation of the response. Both binary and continuous response regression are investigated. An approach to fitting regression trees when covariates are measured with error is described, and the boosting algorithms consist of its repeated application. The main feature of the approach is that it handles situations where multiple covariates are measured with error. Some simulation results are given as well as its application to data from the Framingham Heart Study.