Adaptive estimation under single-index constraint in a regression model

DOI10.1214/13-AOS1152zbMath1302.62077arXiv1304.7668MaRDI QIDQ2448721

Nora Serdyukova, O. V. Lepskij

Publication date: 5 May 2014

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.7668

zbMATH Keywords

lower boundsadaptive estimationnonparametric regressionoracle inequalitiesminimax ratesingle-index modelstructural adaptation

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Asymptotic properties of nonparametric inference (62G20) Nonparametric estimation (62G05)

Related Items

Nonparametric regression on random fields with random design using wavelet method, Adaptive estimation in the functional nonparametric regression model, Lower bounds in estimation at a point under multi-index constraint, Analysis of the rate of convergence of two regression estimates defined by neural features which are easy to implement, Adaptive estimation under single-index constraint in a regression model, A concentration inequality for a Gaussian process indexed by matrices, \(\mathbb{L}_{p}\) adaptive estimation of an anisotropic density under independence hypothesis, Structural adaptive deconvolution under \({\mathbb{L}_p}\)-losses, High-dimensional index volatility models via Stein's identity, Density estimation on an unknown submanifold, Efficient estimation in single index models through smoothing splines, Structural adaptation in the density model, Aggregating estimates by convex optimization, Adaptive estimation over anisotropic functional classes via oracle approach

Cites Work

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• Upper functions for positive random functionals. I: General setting and Gaussian random functions
• Regression with random design: a minimax study
• Structural adaptation via \(\mathbb L_p\)-norm oracle inequalities
• Universal pointwise selection rule in multivariate function estimation
• Wavelet regression in random design with heteroscedastic dependent errors
• Asymptotic minimax estimation of regression in the additive model
• A constrained risk inequality with applications to nonparametric functional estimation
• Optimal spatial adaptation to inhomogeneous smoothness: An approach based on kernel estimates with variable bandwidth selectors
• Semiparametric methods in econometrics
• Wavelet threshold estimation of a regression function with random design
• Regression in random design and warped wavelets
• On minimax wavelet estimators
• Optimal rates and adaptation in the single-index model using aggregation
• Adaptive estimation under single-index constraint in a regression model
• Model selection for regression on a random design
• Nonlinear Estimation in Anisotropic Multi-Index Denoising. Sparse Case
• On pointwise adaptive curve estimation based on inhomogeneous data
• Asymptotic Properties of Non-Linear Least Squares Estimators
• Nonlinear estimation in anisotropic multi-index denoising