ABSTRACT
Although maximum likelihood estimators (MLEs) are optimal with respect to estimate variances, they are not unbiased. In large samples and even in moderatesized samples, bias is essentially negligible. However, in small samples it becomes a major source of error. In order to eliminate bias in small samples from distributions of the type (1/cr).f[(x - t.J..)/cr], the method of weighted least squares, based on the Gauss-Markov least-square theorem, was developed. Using this method, best linear unbiased estimators (BLUE) of the location and scale parameters; tJ.. and cr, which employ order statistics in a systematic manner and which have minimum variance in the class of linear unbiased estimators, can be obtained. Some of the major contributors to the development of the theory underlying these estimators have been Lloyd (1952), Teichroew (1956), Ogawa (1957), Sarhan (1954, 1955a, b), Sarhan and Greenberg (1956, 1957, 1958, 1962), David (1970), Gupta (1952), Blom (1956), and numerous others.
