Generalized score tests for missing covariate data

In this dissertation, the generalized score tests based on weighted estimating equationsare proposed for missing covariate data. Their properties, including the effectsof nuisance functions on the forms of the test statistics and efficiency of the tests,are investigated. Different versions of the test statistic are properly defined for variousparametric and semiparametric settings. Their asymptotic distributions are alsoderived. It is shown that when models for the nuisance functions are correct, appropriatetest statistics can be obtained via plugging the estimates of the nuisancefunctions into the appropriate test statistic for the case that the nuisance functionsare known. Furthermore, the optimal test is obtained using the relative efficiencymeasure. As an application of the proposed tests, a formal model validation procedureis developed for generalized linear models in the presence of missing covariates.The asymptotic distribution of the data driven methods is provided. A simulationstudy in both linear and logistic regressions illustrates the applicability and the finitesample performance of the methodology. Our methods are also employed to analyzea coronary artery disease diagnostic dataset.