Minimax properties of gamma kernel density estimators under $L^p$ loss and $β$-Hölder smoothness of the target
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917264843866112 |
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| author | Ouimet, Frédéric |
| author_facet | Ouimet, Frédéric |
| contents | This paper considers the asymptotic behavior in $β$-Hölder spaces, and under $L^p$ loss, of the gamma kernel density estimator introduced by Chen [Ann. Inst. Statist. Math. 52 (2000), 471-480] for the analysis of nonnegative data, when the target's support is assumed to be upper bounded. It is shown that this estimator can achieve the minimax rate asymptotically for a suitable choice of bandwidth whenever $(p,β)\in [1,3)\times(0,2]$ or $(p,β)\in [3,4)\times ((p-3)/(p-2),2]$. It is also shown that this estimator cannot be minimax when either $p\in [4,\infty)$ or $β\in (2,\infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10103 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimax properties of gamma kernel density estimators under $L^p$ loss and $β$-Hölder smoothness of the target Ouimet, Frédéric Statistics Theory Probability 62G07, 62G05, 62G20 This paper considers the asymptotic behavior in $β$-Hölder spaces, and under $L^p$ loss, of the gamma kernel density estimator introduced by Chen [Ann. Inst. Statist. Math. 52 (2000), 471-480] for the analysis of nonnegative data, when the target's support is assumed to be upper bounded. It is shown that this estimator can achieve the minimax rate asymptotically for a suitable choice of bandwidth whenever $(p,β)\in [1,3)\times(0,2]$ or $(p,β)\in [3,4)\times ((p-3)/(p-2),2]$. It is also shown that this estimator cannot be minimax when either $p\in [4,\infty)$ or $β\in (2,\infty)$. |
| title | Minimax properties of gamma kernel density estimators under $L^p$ loss and $β$-Hölder smoothness of the target |
| topic | Statistics Theory Probability 62G07, 62G05, 62G20 |
| url | https://arxiv.org/abs/2602.10103 |