Rodeo: Sparse, greedy nonparametric regression

• 成果类型: Article
• 署名作者: Lafferty, John; Wasserman, Larry
• 署名单位: Carnegie Mellon University; Carnegie Mellon University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000811
• 发表日期: 2008
• 页码: 28-63
• 关键词: nonconcave penalized likelihood; selection

摘要

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.