Linear scale estimation

Abstract

A simple linear estimator for the scale parameter of a location-scale Cauchy distribution is developed, which does not require knowledge of the moments of the distribution. This estimator is shown to have almost minimum mean squared-error, even for small samples. It is also shown to give good starting values for finding the maximum likelihood estimator by iterative methods. This method is then extended to the logistic and normal distributions.

Keywords:

• Cauchy distribution
• minimum mean squared-error
• minimum variance
• order statistics

^∗Department of Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Manitoba R3B 2E9.

^∗Department of Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Manitoba R3B 2E9.

Notes

^∗Department of Statistics, University of Winnipeg, 515 Portage Avenue, Winnipeg, Manitoba R3B 2E9.