The Annals of Statistics
- Ann. Statist.
- Volume 41, Number 1 (2013), 41-62.
Spatially-adaptive sensing in nonparametric regression
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.
Ann. Statist., Volume 41, Number 1 (2013), 41-62.
First available in Project Euclid: 5 March 2013
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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
- Supplementary material: Proofs for “Spatially-adaptive sensing in nonparametric regression”. We provide detailed proofs of the results in this paper.