Abstract
This paper deals with the non-parametric estimation in the regression with the multiplicative noise. Using the local polynomial fitting and the bayesian approach, we construct the minimax on isotropic Hölder class estimator. Next, applying Lepski’s method we propose an estimator which is optimally adaptive over the collection of isotropic Hölder classes. To prove the optimality of the proposed procedure, we establish in particular the exponential inequality for the deviation of locally bayesian estimator since the parameter estimated. These theoretical results are illustrated by simulation study.
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Chichignoud, M. Minimax and minimax adaptive estimation in multiplicative regression: locally bayesian approach. Probab. Theory Relat. Fields 153, 543–586 (2012). https://doi.org/10.1007/s00440-011-0354-7
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DOI: https://doi.org/10.1007/s00440-011-0354-7
Keywords
- Local bayesian fitting
- Multiplicative regression
- Adaptive bandwidth selector
- Lepski’s method
- Optimality criterion