The limiting variance function for design sequences

Abstract

PAZMAN [2] shows that for a linear regression model and an arbitrary sequences of design points the variance of the least squares estimate, based on observations up to x _n tends to zero as n tends to infinity. Here, the whole sequence of variance functions is investigated. It is shown that the sequence converges uniformly to a continuous function which is zero at any limit point of the sequence {x _n }. PAZMAN's result is thus a special case. Such results are useful for optimum design algorithms and give a sufficiency condition for consistency of LS estimators.