Abstract
In this paper we establish an optimal asymptotic linear predictor which does not involve the finite-sample variance-covariance structure. Extensions to the problem of finding the best linear unbiased and simple linear unbiased predictors for k samples are given. Moreover, we obtain alternative linear predictors by modifying the covariance matrix by either an identity matrix or a diagonal matrix. For normal, logistic and Rayleigh samples of size 10, the alternative linear predictors with these modifications have high efficiency when compared with the best linear unbiased predictor.