Rodeo: Sparse Nonparametric Regression in High Dimensions
John Lafferty and Larry Wasserman
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
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.
Keywords: Nonparametric regression, sparsity, local linear
smoothing, adaptive estimation, bandwidth estimation, variable selection.