Abstract
In this paper, we derive asymptotic expressions for the mean integrated squared error of a class of delta sequence density estimators for circular data. This class includes the class of kernel density estimators usually considered in the literature, as well as a new class that is closer in spirit to the class of Parzen–Rosenblatt estimators for linear data. For these two classes of kernel density estimators, a Fourier series-based direct plug-in approach for bandwidth selection is presented. The proposed bandwidth selector has a relative convergence rate whenever the underlying density is smooth enough and the simulation results testify that it presents a very good finite sample performance against other bandwidth selectors in the literature.
Acknowledgments
The author would like to thank the anonymous reviewers and associate editor for their constructive comments and suggestions that greatly helped to improved this work.
Disclosure statement
No potential conflict of interest was reported by the author(s).