|Institution:||Texas A&M University|
|Keywords:||Data driven method; Generalized score test; Goodness of fit; Nuisance function; Missing at random; Weighted estimating equation.|
|Full text PDF:||http://hdl.handle.net/1969.1/ETD-TAMU-1625|
In this dissertation, the generalized score tests based on weighted estimating equations are proposed for missing covariate data. Their properties, including the effects of 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 various parametric and semiparametric settings. Their asymptotic distributions are also derived. It is shown that when models for the nuisance functions are correct, appropriate test statistics can be obtained via plugging the estimates of the nuisance functions into the appropriate test statistic for the case that the nuisance functions are known. Furthermore, the optimal test is obtained using the relative efficiency measure. As an application of the proposed tests, a formal model validation procedure is developed for generalized linear models in the presence of missing covariates. The asymptotic distribution of the data driven methods is provided. A simulation study in both linear and logistic regressions illustrates the applicability and the finite sample performance of the methodology. Our methods are also employed to analyze a coronary artery disease diagnostic dataset.