Testing linear restrictions on parameters of linear model under heteroscedasticity

A large number of problems in Applied Regression Analysis are concerned with the estimation of regression coefficients in the linear regression models subject to linear restrictions. Efficient estimation of linear models under linear restrictions on parameters has received little attention. Generally linear equality or inequality restrictions may be incorporated in the process of estimation of linear statistical models. These restrictions may be either exact or stochastic models. These restrictions may be either exact or stochastic in nature and they give additional or extraneous information about regression coefficients. Objective of the paper is to describe the inferential problems in linear regression models subject to some linear equality restrictions. A generalized linear model with non-spherical disturbances has been specified with exact linear restrictions about the parameters. Later, the maximum likelihood estimation has applied to estimate unknown covariance matrix of disturbances and then estimated the parameters of linear regression model. MSE criterion has been proposed to test for the better performance of the restricted estimated GLS (EGLS) estimators over that of unrestricted estimators of the regression coefficients.