SB-Robust Estimators of the Parameters of the Wrapped Normal Distribution

Abstract

In this article, we study the SB-robustness of various estimators of the mean direction (μ) and the concentration parameter (ρ) of the wrapped normal distribution. The functional corresponding to the sample mean direction is seen to be not SB-robust as an estimator of μ at the family of wrapped normal distributions with varying ρ, whereas the γ-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 ρ and also that for a newly introduced trimmed estimator of ρ.

Keywords:

• Circular data
• Concentration
• Circular mean direction
• Equivalent measures of dispersion
• SB-robustness
• Trimmed mean direction
• Wrapped normal distribution

Mathematics Subject Classification:

• 62G35
• 62H11

Acknowledgment

The authors are grateful to the anonymous referees for their valuable suggestions which helped them in improving this article.