On the optimum best linear unbiased estimates of the parameters of the normal distribution based on selected order statistics

Abstract

Abstract Let be the order statistics in an ordered random sample of size n from the normal population N(±, σ2 with mean ± and standard deviation σ. The present paper (1) provides the optimum ranks coefficients and efficiencies of Lloyd's [6] best linear unbiased estimates (BLUE) of ±, σ (when one is known) and (±, σ) based on the k = 1,2, 3, 4 order statistics selected from (Ll) which give the highest efficiencies and (2) demonstrates that efficiencies are only slightly reduced if the BLUE of ± and σ (when one is known) based on the order statistics with ranks are replaced by the BLUE based on the order statistics with ranks , where are the optimum spacings for Ogawa's [8] asymptotic best linear estimates (ABLE) of ± and σ when one parameter is known, or even are replaced directly by the ABLE with their corresponding optimum spacings.