This proposal addresses modeling and estimation problems that arise with missing data and/or mismeasured variables. The project consists of three major areas: Frequentist Multiple Imputation Procedures}: The research will consider parametric, nonparametric and semiparametric approaches. The problem to be addressed include proposing new methods of imputation, deriving the properties of the resulting estimators, proposing a method to compare the efficiencies among the procedures and developing inference procedures. The goals are (1) providing the most efficient multiple imputation procedure for parametric and semiparametric models and (2) developing inference procedures for the less efficient but most easily implemented estimators. Measurement error problems in mixed effects pharmacokinetics models: The goals for this research area include (1) determining the effect of measurement errors for both classical measurement error models and the Berkson type of measurement error models, (2) developing graphical tools which can be used to detect the severity of the measurement error effects and (3) providing methods which adjust for the measurement errors for both the classical and the clinical pharmacokinetics models. The study will contain theoretical asymptotic analysis supplemented by extensive simulations and real-data applications. Resampling methods in data-driven smoothing parameter determination: This research will generalize the bootstrap method of Wang (1996) for semi-parametric heteroscedastic regression models to semiparametric procedures which analyze data with missing/mismeasured variables. Because of the technical difficulties, the smoothing parameters for most of the semiparametric procedures have often been determined by ad hoc methods. The approaches proposed will be easy to implement and estimate the smoothing parameters in an automatic fashion. The success of this research will help to promote the use of semiparametric procedures.
