Minimax and minimax adaptive estimation in multiplicative regression: locally Bayesian approach

DOI10.1007/s00440-011-0354-7zbMath1318.62128arXiv1006.0024OpenAlexW2963713752MaRDI QIDQ714947

Michaël Chichignoud

Publication date: 12 October 2012

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.0024

zbMATH Keywords

optimality criterionLepski's methodadaptive bandwidth selectorlocal Bayesian fittingmultiplicative regression

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Asymptotic properties of nonparametric inference (62G20)

Related Items (7)

A robust, adaptive M-estimator for pointwise estimation in heteroscedastic regression ⋮ Nonparametric estimation in a regression model with additive and multiplicative noise ⋮ Estimation in nonparametric regression model with additive and multiplicative noise via Laguerre series ⋮ Adaptive estimation in the single-index model via oracle approach ⋮ Pointwise adaptive estimation of a multivariate function ⋮ Adaptation to lowest density regions with application to support recovery ⋮ Adaptive estimation over anisotropic functional classes via oracle approach

Cites Work

• Unnamed Item
• Unnamed Item
• Minimax theory of image reconstruction
• Structural adaptation via \(\mathbb L_p\)-norm oracle inequalities
• Universal pointwise selection rule in multivariate function estimation
• Nonparametric estimation of composite functions
• Risk bounds for model selection via penalization
• Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes
• Adaptive hypothesis testing using wavelets
• Optimal spatial adaptation to inhomogeneous smoothness: An approach based on kernel estimates with variable bandwidth selectors
• Optimal pointwise adaptive methods in nonparametric estimation
• Propagation-separation approach for local likelihood estimation
• Asymptotically Minimax Adaptive Estimation. I: Upper Bounds. Optimally Adaptive Estimates
• Asymptotically Minimax Adaptive Estimation. II. Schemes without Optimal Adaptation: Adaptive Estimators
• Bandwidth Choice for Average Derivative Estimation
• Spatially Adaptive Estimation via Fitted Local Likelihood Techniques
• On a Problem of Adaptive Estimation in Gaussian White Noise

This page was built for publication: Minimax and minimax adaptive estimation in multiplicative regression: locally Bayesian approach