Some quasi-arithmetic means of random variables easily give unbiased strongly consistent closed-form estimators of the joint of the location and scale parameters of the Cauchy distribution. The one-step estimators of those quasi-arithmetic means of the Cauchy distribution are considered. We establish the Bahadur efficiency of the maximum likelihood estimator and the one-step estimators. We also show that the rate of the convergence of the mean-squared errors achieves the Cramer-Rao bound. Our results are also applicable to the circular Cauchy distribution.

翻译：一些随机变数的准定量手段很容易为Cauchy分布点的位置和比例参数的组合提供不偏袒的、强烈一致的封闭式估计器;考虑Cauchy分布点的这些准定量手段的一阶估计器;我们确定最大可能性估测器和一阶估测器的巴哈德尔效率;我们还表明,中度差错的汇合率达到了Cramer-Rao的界限;我们的结果也适用于Cauchy循环分布。