Abstract
We consider the nonparametric functional estimation of the drift of a Gaussian process via minimax and Bayes estimators. In this context, we construct superefficient estimators of Stein type for such drifts using the Malliavin integration by parts formula and superharmonic functionals on Gaussian space. Our results are illustrated by numerical simulations and extend the construction of James-Stein type estimators for Gaussian processes by Berger and Wolpert [J. Multivariate Anal. 13 (1983) 401-424]. © Institute of Mathematical Statistics, 2008.
| Original language | English |
|---|---|
| Pages (from-to) | 2531-2550 |
| Journal | Annals of Statistics |
| Volume | 36 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - Oct 2008 |
Research Keywords
- Gaussian space
- Harmonic analysis
- Malliavin calculus
- Nonparametric drift estimation
- Stein estimation
Publisher's Copyright Statement
- COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: © Institute of Mathematical Statistics, 2008. Privault, N., & Réveillac, A. (2008). Stein estimation for the drift of Gaussian processes using the Malliavin calculus. Annals of Statistics, 36(5), 2531-2550. https://doi.org/10.1214/07-AOS540.