Abstract
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.
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References
Carlitz L (1962) The inverse of the error function. Pac J Math 13: 459–470
Hampel FR (1974) The influence curve and its role in robust estimation. J Am Stat Assoc 69: 383–393
Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA (1986) Robust statistics. Wiley, New York
Hill GW (1976) New approximations to the von Mises distribution. Biometrika 63(3): 673–676
Jammalamadaka SR, SenGupta A (2001) Topics in circular statistics. World Scientific, Singapore
Ko D (1992) Robust estimation of the concentration parameter of the von Mises—Fisher distribution. Ann Stat 20: 917–928
Ko D, Guttorp P (1988) Robustness of estimators for directional data. Ann Stat 16: 609–618
Mardia KV, Jupp PE (2000) Directional statistics. Wiley, Chichester
Rousseeuw PJ (1981) A new infinitesimal approach to robust estimation. Z Wahrsch verw Gebiete 56: 127–132
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Laha, A.K., Mahesh, K.C. SB-robust estimator for the concentration parameter of circular normal distribution. Stat Papers 53, 457–467 (2012). https://doi.org/10.1007/s00362-010-0352-3
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DOI: https://doi.org/10.1007/s00362-010-0352-3