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arXiv · 2512.07380

Nonparametric optimal density estimation for censored circular data

Nicolas Conanec·Claire Lacour·Thanh Mai Pham Ngoc
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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.

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Nicolas Conanec, Claire Lacour, Thanh Mai Pham Ngoc. 2025-12-08. Nonparametric optimal density estimation for censored circular data. https://arxiv.org/abs/2512.07380

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