Minimax pointwise estimation of an anisotropic regression function with unknown density of the design

DOI10.3103/S1066530711010030zbMath1282.62076OpenAlexW1979949773MaRDI QIDQ2437993

Armelle Guillou, Nicolas Klutchnikoff

Publication date: 10 March 2014

Published in: Mathematical Methods of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1066530711010030

zbMATH Keywords

minimax approachnonparametric regressionrandom designanisotropic Hölder spacesdegenerate design

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Nonparametric estimation (62G05)

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Cites Work

• Universal pointwise selection rule in multivariate function estimation
• Consistent nonparametric regression. Discussion
• Curve estimation when the design density is low
• Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice
• Design adaptive nearest neighbor regression estimation
• Asymptotically Minimax Adaptive Estimation. I: Upper Bounds. Optimally Adaptive Estimates
• Approximation Theorems of Mathematical Statistics
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