Honest adaptive confidence bands and self-similar functions

DOI10.1214/12-EJS720zbMath1295.62049arXiv1110.4985OpenAlexW2169550832WikidataQ109040203 ScholiaQ109040203MaRDI QIDQ1950870

Adam D. Bull

Publication date: 28 May 2013

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.4985

zbMATH Keywords

adaptationconfidence setsself-similar functionsnonparametric statisticssupremum norm

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Density estimation (62G07) Asymptotic properties of nonparametric inference (62G20) Nonparametric tolerance and confidence regions (62G15)

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Cites Work

• Unnamed Item
• Unnamed Item
• On adaptive inference and confidence bands
• Effect of bias estimation on coverage accuracy of bootstrap confidence intervals for a probability density
• Risk bounds for model selection via penalization
• Wavelets on the interval and fast wavelet transforms
• Asymptotic equivalence of nonparametric regression and white noise
• On nonparametric confidence intervals
• Wavelets, approximation, and statistical applications
• On the Frisch-Parisi conjecture
• An adaptation theory for nonparametric confidence intervals
• Honest confidence regions for nonparametric regression
• Adaptive confidence interval for pointwise curve estimation.
• A Smirnov-Bickel-Rosenblatt theorem for compactly-supported wavelets
• Confidence bands in density estimation
• Adaptive confidence bands
• The Construction of Orthonormal Wavelets Using Symbolic Methods and a Matrix Analytical Approach for Wavelets on the Interval
• Minimax Testing of Nonparametric Hypotheses on a Distribution Density in the $L_p$ Metrics
• Ten Lectures on Wavelets
• Simple Regularity Criteria for Subdivision Schemes
• On the Periodized Square ofL²Cardinal Splines
• Introduction to nonparametric estimation

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