Bahadur efficiency of the maximum likelihood estimator and one-step estimator for quasi-arithmetic means of the Cauchy distribution

Yuichi Akaoka (), Kazuki Okamura () and Yoshiki Otobe ()
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Yuichi Akaoka: Shinshu University
Kazuki Okamura: Shizuoka University
Yoshiki Otobe: Shinshu University

Annals of the Institute of Statistical Mathematics, 2022, vol. 74, issue 5, No 3, 895-923

Abstract: Abstract 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 .

Keywords: Bahadur efficiency; Cauchy distribution; Maximum likelihood estimator; One-step estimator (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10463-021-00818-y

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