Semiparametric Partially Linear Regression Models With Missing Data

This dissertation studies a semiparametric partially linear regressionmodel with missing response variable and develops semiparametric efficientinference for the parametric component of the model.The missingnessconsidered here includes a broad range of missing patterns.For the estimationmethod,we use the concept of least favorable curve,least favorable directionand the generalized profile likelihood in Severini and Wong.Asymptoticdistributions for the estimators of the parametic components are obtained.It isshown that the estimators are asymptotically normally distributed under someconditions.Furthermore,we prove that the asymptotic covariance of theestimators achieves the semiparametric lower bound under the regularityconditions and additional conditions.We also propose an algorithm which runsiteratively between fitting parametric components and fitting nonparametriccomponents while holding the other fixed.EM algorithms are used inestimating the parametric components by a semiparametric estimatingequation and in estimating the nonparametric components by smoothingmethods.It is proved that the estimators from this iterative algorithm equal tothe conditional expectations(conditioned on observed data)of thesemiparametric efficient estimators from complete data.The methodology isillustrated and evaluated by numerical examples.