Structural adaptation via L_p-norm oracle inequalities

2007/04/19 by A. Goldenhsluger, Goldenhsluger, A., Oleg Lepski +2 · 2 citations
Computer Science · Decision Sciences · Engineering · Mathematics · #62G05 #62G20 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Optimization and Variational Analysis #Probabilistic and Robust Engineering Design #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #msc:62G05 #msc:62G20 #stat.TH

paper · pdf · doi:10.48550/arxiv.0704.2492

arxiv created 2007/04/19 · openalex publication_date 2007/04/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we study the problem of adaptive estimation of a multivariate function satisfying some structural assumption. We propose a novel estimation procedure that adapts simultaneously to unknown structure and smoothness of the underlying function. The problem of structural adaptation is stated as the problem of selection from a given collection of estimators. We develop a general selection rule and establish for it global oracle inequalities under arbitrary \rL_p--losses. These results are applied for adaptive estimation in the additive multi--index model.

Citations

• Asymptotic Properties of Non-Linear Least Squares Estimators

Cited by

• Upper functions for L_p-norm of gaussian random fields
• Nonparametric Denoising of Signals with Unknown Local Structure, I: Oracle Inequalities

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