V-robustezza approssimata

Optinality of OLS estimators of a linear model's parameters may be attained if and only if the covariance structure of the stochastic error has a special pattern. Rao (1967) and Zyskind (1967) gave a complete characterization of this pattern. This paper evaluates the lack of efficiency of OLS vs. WLS estimators of an estimable linear function of parameters caused by a modification ot that patterned covariance matrix W; in particular a perturbating increment rG, of width r and arbitrary direction G is considerd. It is proved that the lack of efficiency is of second order w.e. to r. This result proves a previous one stated, without explicit proof in Kiefer, Wynn (1981). An interesting application is finally proposed for fractional factorial designs.