Pretest and shrinkage Estimation of the regression parameter vector of the marginal model with multinomial responses

One of the main tasks in regression analysis is to draw inference about the regression parameters vector. In this research project, we will consider regression models with multinomial responses in which the response variable takes any value in a set of different nominal or ordinal categories. We will employ the Generalized Estimating Equations (GEE) method to obtain an estimate of the regression parameter vector (). An improvement of this estimator in terms of the mean squared error (MSE) using the idea of the pretest and shrinkage estimation techniques will be considered. All estimators will be compared analytically via their asymptotic quadratic risks, and numerically via their MSEs using Monte Carlo Simulation experiments. A real data example will also be used to compare the array of estimators using a bootstrapping method