Abstract: In this paper we propose an estimator for the function where bis the scale parameter
of the Cauchy distribution. The estimator is obtained by equating the sample
moment of to the corresponding
population moment. We show that the estimator is unbiased, consistent and
asymptotically normally distributed. The efficiency of our estimator is compared
to the maximum likelihood and to quantiles based estimators. It turns out that
this estimator is superior, in terms of asymptotic efficiency, to the quantiles
estimator and competing well with the maximum likelihood estimator for a
reasonable class of b. Finally, we compare
the power of test statistics based on the proposed estimator to those based on
maximum likelihood and on quantiles.
Keywords and phrases: Cauchy distribution, moment-type estimator, quantile estimator, maximum likelihood estimator, asymptotic relative efficiency.
