In this paper we discuss robust estimation of the concentration parameter (κ) of the circular normal (CN) distribution. It is known that the MLE of the concentration parameter is not B-robust at the family of all circular normal distributions with fixed mean direction (μ) and varying κ > 0. In this paper we propose a new estimator for κ and show that it is B-robust and SB-robust at the family {CN (μ, κ) : m ≤ κ ≤ M} where m and M are two arbitrary constants.
In this article, we study the SB-robustness of various estimators of the mean direction and the concentration parameter of the wrapped normal distribution. The functional corresponding to the sample mean direction is seen to be not SB-robust as an estimator of at the family of wrapped normal distributions with varying , whereas the -trimmed mean direction is SB-robust at the same family of distributions for the different dispersion measures considered in this article.We also study the SB-robustness of the moment estimator of and also that for a newly introduced trimmed estimator of .
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