Nearly Best Linear Unbiased Estimators of the Location and Scale Parameters of the Cauchy Distribution by the Use of Censored Order Statistics

摘要

The Nearly Best Linear Unbiased Estimators (NBLE or NBLUE) of location (mu) and scale parameter (sigma) is developed and applied to the Cauchy distribution for N=15(1)40. For the Cauchy the first and last two order statistics are always censored. Estimator coefficients and relative efficiencies with respect to the minimally censored samples are developed for (1) additional censoring symmetrically from above and below and (2) additional censoring from above only. The idiosyncrasies of the Cauchy are explored along with the efficiencies and applicability of other alternative procedures. (Author)