Abstract: The present paper discusses the relative efficiencies of the least square estimates in linear models. For Gauss-Markoff model:Y=X_e + e,E(e)=0, Cov(e)=σ²V, an new efficiency of least square estimate for linearly estimable function c' τ is proposed and its lower bound is given. For variance component model:Y=Xτ+ e, E(e)=0, Cov(e)=∑_i=1^mσ²V, an new efficiency of least square estimate for linearly estimable function c' τ is introduced for the first time and its lower bound, which is independent of unknown parameters, is also obtained.

Key words: Linear model, Gauss-Markov, Variance component, LSE, BLUE, Efficiency