We present a method for simultaneously performing bandwidth selection
and variable selection in nonparametric regression. The method starts
with a local linear estimator with large bandwidths, and
incrementally decreases the bandwidth in directions where the gradient
of the estimator with respect to bandwidth is large. When the unknown
function satisfies a sparsity condition, the approach avoids the curse
of dimensionality. The method---called rodeo(regularization
of derivative expectation operator)---conducts a sequence of
hypothesis tests, and is easy to implement. A modified version that
replaces testing with soft thresholding may be viewed as solving a
sequence of lasso problems. When applied in one dimension, the rodeo
yields a method for choosing the locally optimal bandwidth.
Joint work with John Lafferty.
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Pradeep Ravikumar Last modified: Fri Mar 31 00:50:20 EST 2006