Abstract
We propose a block-resampling penalization method for marginal density estimation with nonnecessary independent observations. When the data are β or τ -mixing, the selected estimator satisfies oracle inequalities with leading constant asymptotically equal to 1. We also prove in this setting the slope heuristic, which is a data-driven method to optimize the leading constant in the penalty.
| Original language | English |
|---|---|
| Pages (from-to) | 1852-1877 |
| Number of pages | 26 |
| Journal | Annals of Statistics |
| Volume | 39 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Aug 2011 |
| Externally published | Yes |
Keywords
- Density estimation
- Optimal model selection
- Resampling methods
- Slope heuristic
- Weak dependence.