Limit theorems for quasi-arithmetic means of random variables with applications to point estimations for the Cauchy distribution-Reference-Cited by-同舟云学术

Limit theorems for quasi-arithmetic means of random variables with applications to point estimations for the Cauchy distribution

Published:2022-06-01 Issue:2 Volume:36 Page:
ISSN:0103-0752
Container-title:Brazilian Journal of Probability and Statistics
language:
Short-container-title:Braz. J. Probab. Stat.

Author:

Akaoka Yuichi¹,Okamura Kazuki²,Otobe Yoshiki¹

Affiliation:

1. Shinshu University, 3-1-1, Asahi, Matsumoto, Nagano, Japan

2. Shizuoka University, 836, Ohya, Suruga-ku, Shizuoka, Japan

Publisher

Institute of Mathematical Statistics

Subject

Statistics and Probability

Reference57 articles.

1. Aczél, J. (1948). On mean values. Bulletin of the American Mathematical Society 54, 392–400.

2. Akaoka, Y. (2020). Parameter estimation using complex valued moments for Cauchy distributions. Master’s thesis, Department of mathematics, Shinshu University.

3. Akaoka, Y., Okamura, K. and Otobe, Y. (2021). Confidence disc for Cauchy distributions. Preprint.

4. Akaoka, Y., Okamura, K. and Otobe, Y. (2022). Bahadur efficiency of the maximum likelihood estimator and one-step estimator for quasi-arithmetic means of the Cauchy distribution. Annals of the Institute of Statistical Mathematics.

5. Arslan, O. and Kent, J. T. (1998). A note on the maximum likelihood estimators for the location and scatter parameters of a multivariate Cauchy distribution. Communications in Statistics Theory and Methods 27, 3007–3014.

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