On nonparametric estimation and inference with censored data, bandwidth selection for local polynomial regression, and subset selection in explanatory regression analyse

We address several problems in different but related areas of biostatistics. A new model selection criterion is proposed for selecting a good set of confounders to include in a linear model when interest is focused on estimation of particular adjusted associations rather than predicted values. New estimates of the bias, variance, and MSE-optimal bandwidth in local polynomial regression are proposed, and Monte Carlo simulations demonstrate their excellent finite-sample performance. Solutions are also provided to the problems of (1) bandwidth selection, smooth estimation, and inference for the distribution and density functions with interval censored data; (2) construction of confidence intervals for moments and other smooth functionals with interval censored data; and (3) efficient nonparametric estimation of the distributions of onset and lifetime associated with an irreversible disease that is only detectable at sacrifice or death.;We present a new, data-driven method in Chapter 1 for automatically choosing a good subset of potential confounding variables to include in an explanatory linear regression model. This same model selection scheme can also be used in a less focused analysis to simply identify those variables which are jointly related to the response.;In Chapter 2, we study the performance of data-driven bandwidth selectors for local polynomial regression. These bandwidth selection procedures are based on minimizing estimated "pre-limit" approximations to the mean squared error.;Data-adaptive smooth estimation of the survival function and construction of confidence limits with interval censored data are open problems. In Chapter 3, we provide solutions to these problems, including the important generalization to the estimation of the density and its derivatives, assuming that the observed monitoring times are independent of the time of interest T.;In Chapter 4, we provide a simple method for constructing confidence intervals for smooth functionals of the survival function based on interval censored data. Since the nonparametric maximum likelihood estimator (NPMLE) of the survival function is highly implicit, the asymptotic distributions of efficient estimators of smooth functionals based on its integrated form have yet to be derived.;Chapter 5 is devoted to the study of efficient estimation of the distribution of onset and lifetime associated with an irreversible disease that is only detectable at sacrifice or death. (Abstract shortened by UMI.).