  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.
