2005/06/17 by John Lafferty, Larry Wasserman, Lafferty, John +1 · 1 citation
Computer Science · Mathematics · #62G08 #Bayesian Methods and Mixture Models #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62G08 #stat.TH
paper · pdf · doi:10.48550/arxiv.math/0506342
openalex publication_date 2005/06/17 · arxiv created 2006/08/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.