Rodeo: Sparse, greedy nonparametric regression

Details Rodeo: Sparse, greedy nonparametric regression Rodeo: Sparse, greedy nonparametric regression

2008-03-12

arxiv.org/abs/0803.1709v1

Annals of Statistics 2008, Vol. 36, No. 1, 28-63

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000811 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053607000000811

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.

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