This paper aims at the method of OLS 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 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 variance-covariance matrix of BLUE are discussed. Moreover generalized Gauss-Markoff theorem for linear estimation, characteristic properties of OLS estimators and problems of linear statistical model by violating the assumptions are extensively discussed.
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