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Minimax bounds for Besov classes in density estimation
| Content Provider | Hyper Articles en Ligne (HAL) |
|---|---|
| Author | Sart, Mathieu |
| Copyright Year | 2021 |
| Abstract | We study the problem of density estimation on $[0,1]$ under $\mathbb{L}^p$ norm. We carry out a new piecewise polynomial estimator and prove that it is simultaneously (near)-minimax over a very wide range of Besov classes $\mathcal{B}_{\pi,\infty}^{\alpha}(R)$. In particular, we may deal with unbounded densities and shed light on the minimax rates of convergence when $\pi |
| Related Links | https://hal.science/hal-02550114v3/file/ArticleHal.pdf |
| e-ISSN | 19357524 |
| DOI | 10.1214/21-EJS1856 |
| Journal | Electronic Journal of Statistics |
| Issue Number | 1 |
| Volume Number | 15 |
| Language | English |
| Publisher | HAL CCSD Shaker Heights, OH : Institute of Mathematical Statistics |
| Publisher Date | 2021-01-01 |
| Access Restriction | Open |
| Subject Keyword | December minimax risk Besov spaces Mathematics [math] Statistics [math.ST] |
| Content Type | Text |
| Resource Type | Article |
| Subject | Statistics, Probability and Uncertainty Statistics and Probability Mathematics |
