Rodeo: Sparse, greedy nonparametric regression
John Lafferty and Larry Wasserman
Source: Ann. Statist. Volume 36, Number 1 (2008), 28-63.
Abstract
We present a greedy method for simultaneously performing local bandwidth selection and variable selection in nonparametric regression. The method starts with a local linear estimator with large bandwidths, and incrementally decreases the bandwidth of variables for which the gradient of the estimator with respect to bandwidth is large. The method—called rodeo (regularization of derivative expectation operator)—conducts a sequence of hypothesis tests to threshold derivatives, and is easy to implement. Under certain assumptions on the regression function and sampling density, it is shown that the rodeo applied to local linear smoothing avoids the curse of dimensionality, achieving near optimal minimax rates of convergence in the number of relevant variables, as if these variables were isolated in advance.
Primary Subjects: 62G08
Secondary Subjects: 62G20
Keywords: Nonparametric regression; sparsity; local linear smoothing; bandwidth estimation; variable selection; minimax rates of convergence
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1201877293
Digital Object Identifier: doi:10.1214/009053607000000811
Mathematical Reviews number (MathSciNet):
MR2387963
Zentralblatt MATH identifier:
1132.62026
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