Use of Quasi-Ranges in the Estimation of Scale Parameter of a Symmetric Distribution

Abstract

In this article, we consider the problem of best linear unbiased estimation and best linear invariant estimation of the scale parameter of a symmetric distribution using quasi-ranges is considered. We also prove a sufficient condition for the non negativity of the scale estimator obtained by the above method. Further, we obtain necessary and sufficient conditions for the derived estimators to be constant multiple of the sample range.

Keywords:

• Best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs)
• Location-scale family
• Order statistics of independent identically distributed (iid) random variables
• Quasi-ranges

2000 Mathematics Subject Classification:

• Primary 62G30
• Secondary 62G05