Nonparametric regression in exponential families

DOI10.1214/09-AOS762zbMath1202.62050arXiv1010.3836MaRDI QIDQ987997

Harrison H. Zhou, Lawrence D. Brown, T. Tony Cai

Publication date: 24 August 2010

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

Full work available at URL: https://arxiv.org/abs/1010.3836

zbMATH Keywords

waveletsJames-Stein estimatoradaptivityexponential familyasymptotic equivalencequadratic variance functionquantile couplingnonparametric Gaussian regression

Mathematics Subject Classification ID

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

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Cites Work

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• On the construction of classes of variance stabilizing transformations
• The root-unroot algorithm for density estimation as implemented via wavelet block thresholding
• Robust nonparametric estimation via wavelet median regression
• Mapping properties of nonlinear operators in spaces of Triebel-Lizorkin and Besov type
• Natural exponential families with quadratic variance functions
• A constrained risk inequality with applications to nonparametric functional estimation
• Adaptive wavelet estimation: A block thresholding and oracle inequality approach
• Block threshold rules for curve estimation using kernel and wavelet methods
• Transformation theory: How normal is a family of distributions?
• Wavelet shrinkage for natural exponential families with quadratic variance functions
• A User's Guide to Measure Theoretic Probability
• Interpolation of Besov Spaces
• Ten Lectures on Wavelets
• An approximation of partial sums of independent RV'-s, and the sample DF. I
• Ideal spatial adaptation by wavelet shrinkage
• Nonparametric Wavelet Regression for Binary Response
• Bayesian Multiscale Models for Poisson Processes
• Wavelets and Dilation Equations: A Brief Introduction
• A Comparative Simulation Study of Wavelet Shrinkage Estimators for Poisson Counts
• Negative Binomial Regression
• Multiscale generalised linear models for nonparametric function estimation
• Testing Statistical Hypotheses
• Transformations: An Introduction and a Bibliography
• Univariate Discrete Distributions
• THE TRANSFORMATION OF POISSON, BINOMIAL AND NEGATIVE-BINOMIAL DATA