Estimation of regression coefficients and influence functions in multivariate regression models with prior information

摘要

In regression analysis, it is possible that the investigator has prior information about regression coefficients. In such a case, a restricted least squares estimator for the regression coefficients can be constructed using both the sample information and the prior information. In this research, we consider a multivariate regression model with either non-stochastic or stochastic restriction and obtain restricted and mixed estimator of regression coefficients, respectively. We also develop a compatibility test statistic under the multivariate regression model with either non-stochastic or stochastic restriction. A preliminary test estimator is constructed and studied in each case. A comparison of the superiority of the estimator is presented by using the mean square error criterion.;In addition to the estimation for the regression coefficients under restricted models, we also consider the question of whether there exist unusual observations in the sample which strongly affect the estimators. We derive an influence function based on Cook's distance to determine influential observations in a regression model with restriction.