Kernel density estimation for circular data: a Fourier series-based plug-in approach for bandwidth selection

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 which 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 $n^{-1/2}$ 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.