Bounds on chi-square statistics for localized bases with application to optimal estimation
Abstract
We develop new deviation bounds for chi-square statistics that are sharp enough to construct penalties in least-squares density estimation allowing optimal estimation under mild smoothness constraints without imposing assumptions on the density's support or supremum norm. In particular, we establish new minimax rates under conditions that provide a natural transition between compactly supported and infinitely supported densities, as well as between bounded and unbounded ones.
Fields of Study & Subjects
Statistical Methods and Inference
Probability and Statistical Research
Statistical Methods and Applications
Publication details
- Journal / source
- HAL
- Publication date
- 6 February 2026
- Language
- EN
- Document type
- Preprint