Nonparametric optimal density estimation for censored circular data
Abstract
We consider the problem of estimating the probability density function of a circular random variable observed under censoring. To this end, we introduce a projection estimator constructed via a regression approach on linear sieves. We first establish a lower bound for the mean integrated squared error in the case of Sobolev densities, thereby identifying the minimax rate of convergence for this estimation problem. We then derive a matching upper bound for the same risk, showing that the proposed estimator attains the minimax rate when the underlying density belongs to a Sobolev class. Finally, we develop a data-driven version of the procedure that preserves this optimal rate, thus yielding an adaptive estimator. The practical performance of the method is demonstrated through simulation studies.
Cite
@article{arxiv.2512.07380,
title = {Nonparametric optimal density estimation for censored circular data},
author = {Nicolas Conanec and Claire Lacour and Thanh Mai Pham Ngoc},
journal= {arXiv preprint arXiv:2512.07380},
year = {2025}
}