{"ID":2831613,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.07380","arxiv_id":"2512.07380","title":"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.","short_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 So...","url_abs":"https://arxiv.org/abs/2512.07380","url_pdf":"https://arxiv.org/pdf/2512.07380v1","authors":"[\"Nicolas Conanec\",\"Claire Lacour\",\"Thanh Mai Pham Ngoc\"]","published":"2025-12-08T10:16:00Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}