The use of spacings in the estimation of a scale parameter

Abstract

Linear functions on spacings-instead of linear functions on order statistics-are considered, in order to simplify the form of best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) for the scale parameter in the classical location-scale family. Also, a sufficient condition for the non-negativity of the scale estimator is presented and, moreover, necessary and sufficient conditions for the BLUE (and the BLIE) to be a constant multiple of the sample range are derived. Finally, a modification of this approach is applied in order to simplify the derivations of both the location and the scale estimators in the Uniform Type-II Censored model. © 2002 Elsevier Science B.V. All rights reserved.