Identifiability of Asymmetric Circular and Cylindrical Distributions

Yoichi Miyata (), Takayuki Shiohama and Toshihiro Abe
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Yoichi Miyata: Takasaki City University of Economics
Takayuki Shiohama: Nanzan University
Toshihiro Abe: Hosei University

Sankhya A: The Indian Journal of Statistics, 2023, vol. 85, issue 2, No 13, 1451 pages

Abstract: Abstract Identifiability of statistical models is a fundamental and essential condition that is required to prove the consistency of maximum likelihood estimators. The identifiability of the skew families of distributions on the circle and cylinder for estimating model parameters has not been fully investigated in the literature. In this paper, a new method combining the trigonometric moments and the simultaneous Diophantine approximation is proposed to prove the identifiability of asymmetric circular and cylindrical distributions. Using this method, we prove the identifiability of general sine-skewed circular distributions, including the sine-skewed von Mises and sine-skewed wrapped Cauchy distributions, and that of a Möbius transformed cardioid distribution, which can be regarded as asymmetric distributions on the unit circle. In addition, we prove the identifiability of two cylindrical distributions wherein both marginal distributions of a circular random variable are the sine-skewed wrapped Cauchy distribution, and conditional distributions of a random variable on the non-negative real line given the circular random variable are a Weibull distribution and a generalized Pareto-type distribution, respectively.

Keywords: Asymmetric distributions; circular distributions; cylindrical distributions; diophantine approximations; identifiability.; Primary 60E05; Secondary 62E15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13171-022-00294-3

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