Nonparametric optimal density estimation for censored circular data
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911307957010432 |
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| author | Conanec, Nicolas Lacour, Claire Ngoc, Thanh Mai Pham |
| author_facet | Conanec, Nicolas Lacour, Claire Ngoc, Thanh Mai Pham |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07380 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonparametric optimal density estimation for censored circular data Conanec, Nicolas Lacour, Claire Ngoc, Thanh Mai Pham Statistics Theory 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. |
| title | Nonparametric optimal density estimation for censored circular data |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2512.07380 |