Square root penalty: Adaption to the margin in classification and in edge estimation
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Publication:2569239
DOI10.1214/009053604000001066zbMath1080.62047arXivmath/0507422OpenAlexW3099719085MaRDI QIDQ2569239
Sara van de Geer, Alexandre B. Tsybakov
Publication date: 18 October 2005
Published in: The Annals of Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0507422
Nonparametric regression and quantile regression (62G08) Density estimation (62G07) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Pattern recognition, speech recognition (68T10)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Minimax theory of image reconstruction
- Risk bounds for model selection via penalization
- Wavelets, approximation, and statistical applications
- Smooth discrimination analysis
- Empirical margin distributions and bounding the generalization error of combined classifiers
- Penalized blockwise Stein's method, monotone oracles and sharp adaptive estimation
- Complexity regularization via localized random penalties
- Optimal aggregation of classifiers in statistical learning.
- Aggregated estimators and empirical complexity for least square regression
- Local Rademacher complexities and oracle inequalities in risk minimization. (2004 IMS Medallion Lecture). (With discussions and rejoinder)
- Adaptive estimation with soft thresholding penalties
- Rademacher penalties and structural risk minimization
- 10.1162/1532443041424319
- Convexity, Classification, and Risk Bounds
