A note on a Parzen--Rosenblatt type density estimator for circular data

Abstract

Using the close connection between the Parzen-Rosenblatt estimator for linear data and the recently proposed Parzen-Rosenblatt type estimator for circular data, we establish some asymptotic properties of this last estimator, such as asymptotic unbiasedness, weak and strong pointwise consistency, and weak and strong uniform consistency