The Annals of Statistics

Spatially-adaptive sensing in nonparametric regression

Adam D. Bull

Full-text: Open access

Abstract

While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an adaptive-sensing algorithm which is applicable to general nonparametric-regression problems. The algorithm is spatially adaptive, and achieves improved rates of convergence over spatially inhomogeneous functions. Over standard function classes, it likewise retains the spatial adaptivity properties of a uniform design.

Article information

Source
Ann. Statist., Volume 41, Number 1 (2013), 41-62.

Dates
First available in Project Euclid: 5 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aos/1362493039

Digital Object Identifier
doi:10.1214/12-AOS1064

Mathematical Reviews number (MathSciNet)
MR3059409

Zentralblatt MATH identifier
1347.62059

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62L05: Sequential design 62G20: Asymptotic properties

Keywords
Nonparametric regression adaptive sensing sequential design active learning spatial adaptation spatially inhomogeneous functions

Citation

Bull, Adam D. Spatially-adaptive sensing in nonparametric regression. Ann. Statist. 41 (2013), no. 1, 41--62. doi:10.1214/12-AOS1064. https://projecteuclid.org/euclid.aos/1362493039


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