The Annals of Statistics
- Ann. Statist.
- Volume 33, Number 3 (2005), 1203-1224.
Square root penalty: Adaptation to the margin in classification and in edge estimation
A. B. Tsybakov and S. A. van de Geer
Abstract
We consider the problem of adaptation to the margin in binary classification. We suggest a penalized empirical risk minimization classifier that adaptively attains, up to a logarithmic factor, fast optimal rates of convergence for the excess risk, that is, rates that can be faster than n−1/2, where n is the sample size. We show that our method also gives adaptive estimators for the problem of edge estimation.
Article information
Source
Ann. Statist. Volume 33, Number 3 (2005), 1203-1224.
Dates
First available in Project Euclid: 1 July 2005
Permanent link to this document
http://projecteuclid.org/euclid.aos/1120224100
Digital Object Identifier
doi:10.1214/009053604000001066
Mathematical Reviews number (MathSciNet)
MR2195633
Zentralblatt MATH identifier
1080.62047
Subjects
Primary: 62G07: Density estimation
Secondary: 62G08: Nonparametric regression 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20] 68T10: Pattern recognition, speech recognition {For cluster analysis, see 62H30}
Keywords
Binary classification edge estimation adaptation margin penalized classification rule square root penalty sparsity block thresholding
Citation
Tsybakov, A. B.; van de Geer, S. A. Square root penalty: Adaptation to the margin in classification and in edge estimation. Ann. Statist. 33 (2005), no. 3, 1203--1224. doi:10.1214/009053604000001066. http://projecteuclid.org/euclid.aos/1120224100.
