The Efficiency of Adjusted Least Squares in the Linear Functional Relationship

A linear functional errors-in-variables model with unknown slope
parameter and Gaussian errors is considered. The measurement error
variance is supposed to be known, while the variance of errors in
the equation is unknown. In this model a risk bound of asymptotic
minimax type for arbitrary estimators is established. The bound
lies above that one which was found previously in the case of both
variances known. The bound is attained by an adjusted least square
estimator.