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SB-robust estimation of mean direction for some new circular distributions. (English) Zbl 1420.62238
The authors consider the robustness of estimators of the circular mean in models for directional data. Particular models considered are a three-parameter Kato-Jones distribution (obtained by applying a Möbius transformation to the circular normal distribution), a wrapped-$$t$$ distribution, mixtures of these two distributions, and an asymmetric version of the Kato-Jones distribution. The main results of this paper give conditions under which estimators of the circular mean $$\mu$$ do or do not satisfy certain notions of robustness under some given dispersion measures. The estimators considered include the circular mean functional $$\arctan^*\left(\frac{E\sin\Theta}{E\cos\Theta}\right)$$, where $$\arctan^*$$ represents the quadrant-specific inverse of the tangent function, and the circular trimmed mean functional with trimming proportion $$\gamma$$. A numerical comparison of these two estimators is also made, and simulations are used to suggest guidance on a suitable choice of $$\gamma$$. The paper concludes with some examples and applications.
##### MSC:
 62H11 Directional data; spatial statistics 62F35 Robustness and adaptive procedures (parametric inference) 62F10 Point estimation 62E15 Exact distribution theory in statistics
##### Software:
CircStats; circular; Equator
Full Text:
##### References:
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