Linear Estimation of Parameters of the Cauchy Distribution Based on Sample Quantiles.

Asymptotically best linear unbiased estimates (ABLUE) of the location and scale parameters (when both are unknown) of the Cauchy distribution, based on k order statistics selected from a large sample, are considered. It is shown that the joint asymptotic relative efficiency (JARE) of the two estimates is maximized when the sample quantiles are equally spaced, and expressions are derived for the coefficients used in these estimates. In estimating the scale parameter using a reasonably large number of quantiles, it is found that not much weight is attached to the extreme observations or those close to the median. [ABSTRACT FROM AUTHOR]