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- Confidence disc and square for Cauchy distributions(arXiv)
Author : Yuichi Akaoka, Kazuki Okamura, Yoshiki Otobe
Abstract : We will construct a confidence region of parameters for a sample of size N from Cauchy distributed random variables. Although Cauchy distribution has two parameters, a location parameter μ∈R and a scale parameter σ>0, we will infer them at once by regarding them as a single complex parameter γ:=μ+iσ. The region should be a domain in the complex plane, and we will give a simple and concrete formula to give the region as a disc and a square
2. Bahadur efficiency of the maximum likelihood estimator and one-step estimator for quasi-arithmetic means of the Cauchy distribution(arXiv)
Author : Yuichi Akaoka, Kazuki Okamura, Yoshiki Otobe
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 Cramer-Rao bound. Our results are also applicable to the circular Cauchy distribution