A Partially Linear Regression Model for Data from an Outcome-Dependent Sampling Design.

The outcome dependent sampling scheme has been gaining attention in both the statistical literature and applied fields. Epidemiological and environmental researchers have been using it to select the observations for more powerful and cost-effective studies. Motivated by a study of the effect of in utero exposure to polychlorinated biphenyls on children's IQ at age 7, in which the effect of an important confounding variable is nonlinear, we consider a semi-parametric regression model for data from an outcome-dependent sampling scheme where the relationship between the response and covariates is only partially parameterized. We propose a penalized spline maximum likelihood estimation (PSMLE) for inference on both the parametric and the nonparametric components and develop their asymptotic properties. Through simulation studies and an analysis of the IQ study, we compare the proposed estimator with several competing estimators. Practical considerations of implementing those estimators are discussed.

Inference for Seemingly Unrelated Varying-Coefficient Nonparametric Regression Models.

This paper is concerned with the inference of seemingly unrelated (SU) varying-coefficient nonparametric regression models. We propose an estimation for the unknown coefficient functions, which is an extension of the two-stage procedure proposed by Linton, et al. (2004) in the longitudinal data framework where they focused on purely nonparametric regression. We show the resulted estimators are asymptotically normal and more efficient than those based on only the individual regression equation even when the error covariance matrix is homogeneous. Another focus of this paper is to extend the generalized likelihood ratio technique developed by Fan, Zhang and Zhang (2001) for testing the goodness of fit of models to the setting of SU regression. A wild block bootstrap based method is used to compute p-value of the test. Some simulation studies are given in support of the asymptotics. A real data set from an ongoing environmental epidemiologic study is used to illustrate the proposed procedures.

Statistical Inference for Regression Models with Covariate Measurement Error and Auxiliary Information.

We consider statistical inference on a regression model in which some covariables are measured with errors together with an auxiliary variable. The proposed estimation for the regression coefficients is based on some estimating equations. This new method alleates some drawbacks of previously proposed estimations. This includes the requirment of undersmoothing the regressor functions over the auxiliary variable, the restriction on other covariables which can be observed exactly, among others. The large sample properties of the proposed estimator are established. We further propose a jackknife estimation, which consists of deleting one estimating equation (instead of one obervation) at a time. We show that the jackknife estimator of the regression coefficients and the estimating equations based estimator are asymptotically equivalent. Simulations show that the jackknife estimator has smaller biases when sample size is small or moderate. In addition, the jackknife estimation can also provide a consistent estimator of the asymptotic covariance matrix, which is robust to the heteroscedasticity. We illustrate these methods by applying them to a real data set from marketing science.

A Two-Stage Approach for Semilinear In-Slide Models.

The semilinear in-slide models (SLIMs) have been shown to be effective method for normalizing microarray data (Fan, et al. 2004). Using a backfitting method, Fan, Peng and Huang (2005) proposed a profile least squares (PLS) estimation for the parametric and nonparametric components. The general asymptotic properties for their estimator is not developed. In this paper, we consider a new approach, two-stage estimation, which enables us to establish the asymptotic normalities for both of the parametric and nonparametric component estimators. We further propose a plug-in bandwidth selector using the asymptotic normality of the nonparametric component estimator. The proposed method allow for the modeling of the aggregated SLIMs case where we can explicitly show that taking the aggregated information into account can improve both of the parametric and nonparametric component estimator by the proposed two-stage approach. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedures.

Personal coronary risk profiles modify autonomic nervous system responses to air pollution.

OBJECTIVE: We investigated whether PM2.5-mediated autonomic modulation depends on individual coronary risk profiles. METHODS: Five-minute average heart rate (HR) and heart rate variability (HRV, including standard deviation of normal-to-normal intervals [SDNN], square root of the mean squared differences of successive NN intervals [rMSSD], high frequency [HF]) were measured from 24-hour ambulatory electrocardiograms, and personal PM(2.5) exposures were monitored in a prospective study of 10 male boilermakers (aged 34.3 +/- 8.1 years). We used the Framingham score to classify individuals into low (score = 1-3) and high (score = 5-6) risk categories. Mixed-effect models were used for statistical analyses. RESULTS: Each 1-mg/m(3) increase in the preceding 4-hour moving average PM(2.5) was associated with HR increase (5.3 beats/min) and HRV reduction (11.7%, confidence interval [CI] = 6.2-17.1% for SDNN; 11.1%, CI = 3.1-19.1% for rMSSD; 16.6%, CI = 1.5-31.7% for HF). Greater responses (2- to 4-fold differences) were observed in high-risk subjects than in low-risk subjects. CONCLUSIONS: Our study suggests that adverse autonomic responses to metal particulate are aggravated in workers with higher coronary risk profiles.