The Use of Order Statistics in Estimation

Abstract

A survey is given of recent advances, including a number of original contributions by the author, in the use of order statistics to obtain point and interval estimates of the parameters of various statistical populations from complete and from censored samples. In a few cases estimators based on order statistics are the efficient estimators, but more often they are substitute estimators that sacrifice some efficiency in the interest of computational simplicity and/or robustness in the presence of outliers. In life testing, they are often used to obtain estimates of the parameters of the life distribution before all of the items placed on test have failed. Point estimators based on order statistics may be either best linear unbiased estimators, based on all available observations from complete or censored samples or on one or more observations chosen in some optimal manner, or maximum-likelihood estimators, based on censored samples, of a single parameter or of two or more parameters jointly. Interval estimators may be based on percentage points of order statistics or of functions of order statistics, or they may be based on asymptotic variances and covariances of maximum-likelihood estimators. A summary is given of available results, together with a list of references and examples of applications to such problems as estimating the scatter of bullets aimed at a target and the reliability of an electronic device.