The Circular Structural Model
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1981 · Volume 43 · Issue 2
DOI: 10.1111/j.2517-6161.1981.tb01162.x
Abstract
This paper deals with consistent estimation of the structural parameters of the circular structural model. Identifiability is proved and the difficulties of dealing with the structural model in practice mentioned. A uniform distribution is then assumed for the angular variables and maximum likelihood estimation of the parameters examined. Also discussed are use of an approximation to the ratio of modified Bessel functions, asymptotic behaviour of the estimators as the ratio of the circle radius to the underlying structural variance parameter increases, and efficiency of other estimators of the parameters. The circular functional model, and the difficulties associated with it, is briefly mentioned.
Keywords
circular structural model, identifiability, uniform marginal distribution, maximum likelihood estimation, non-central chi-distribution, modified bessel functions, asymptotic behaviour, efficiency
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