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 Cramér–Rao bound. Our results are also applicable to the circular Cauchy distribution .

中文翻译：

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柯西分布的拟算术均值的最大似然估计量和一步估计量的 Bahadur 效率

一些随机变量的拟算术平均值很容易给出柯西分布的位置和尺度参数的联合的无偏强一致封闭式估计量。考虑了柯西分布的那些准算术平均值的一步估计量。我们建立了最大似然估计器和一步估计器的 Bahadur 效率。我们还表明，均方误差的收敛速度达到了 Cramer-Rao 界。我们的结果也适用于圆形柯西分布。