The performance comparison of optimally weighted LS and linear minimum variance estimation for linear model with random input

The performance comparison of the optimally weighted LS estimate and the linear minimum variance estimate for a linear model with random input is presented. In this case optimally weighted LS estimate is not a linear estimate of a parameter given input and observation anymore while linear minimum variance estimate still is. Under a certain conditions on variance matrix invertibility, we show that the optimally weighted LS estimated outperforms the linear minimum variance estimates provided that they have the same a priori information on the parameter being estimated.