Trimmed estimator for circular–circular regression: breakdown properties and an exact algorithm for computation

Abstract

The paper attempts to address the robustness issues in circular–circular regression. The Möbius transformation-based link function for circular–circular regression is considered. Defining the concept of breakdown point in this context, the robustness issues of the estimators in this model are discussed. Maximum trimmed cosine estimator in this context is considered and the breakdown point of the estimator is calculated. An exact polynomial time algorithm is then proposed for the computation of the estimator which makes the methodology useful and readily applicable for empirical datasets. Simulation studies show that the estimator is robust with respect to the outliers. An analysis of real data is performed to illustrate the proposed methodology.

Keywords:

• Computation
• Möbius transformation
• trimmed estimator
• von Mises distribution
• wrapped Cauchy distribution

2020 Mathematics Subject Classifications:

• 62H11
• 62H10

Acknowledgments

The authors wish to thank the Editor, Associate Editor, and the reviewers for their careful reading and constructive suggestions which led to some improvement over an earlier version of the manuscript.

Availability of data and material (data transparency)

It will be made available by the author upon request.

Code availability (software application or custom code)

It will be made available by the author upon request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This project is partially funded by the Government of India as part of the Institute of Eminence scheme. The funding is provided through the Artificial Intelligence and Data science technology cluster under the head Computational Mathematics and data Science lead by Dr. Neelesh S Upadhye, IIT Madras (Ref. no. [SB20210848MAMHRD00858]); Ministry of Human Resource Development. The funders had no role in the methodological development, data analysis, decision to publish, or preparation of the manuscript.