Ordinary least squares estimation of parameters of linear model

Abstract

This research article primarily focuses on the method of ordinary least squares estimation of parameters of linear model. Here an innovative proof of Gauss-Markoff theorem for linear estimation has been presented. An extensive discussion in evaluating Best Linear Unbiased Estimator (BLUE) of a linear parametric function of the classical linear model is made by using the Gauss-Markoff theorem. Furthermore the importance of mean vector and covariance matrix of BLUE is discussed. Moreover generalized Gauss-Markoff theorem for linear estimation, properties of OLS estimators and problems of linear model by violating the assumptions are extensively discussed.