NDLI: Variable selection in a class of single-index models

Content Provider	Springer Nature Link
Author	Zhu, Li Ping Qian, Lin Yi Lin, Jin Guan
Copyright Year	2010
Abstract	In this paper we discuss variable selection in a class of single-index models in which we do not assume the error term as additive. Following the idea of sufficient dimension reduction, we first propose a unified method to recover the direction, then reformulate it under the least square framework. Differing from many other existing results associated with nonparametric smoothing methods for density function, the bandwidth selection in our proposed kernel function essentially has no impact on its root-n consistency or asymptotic normality. To select the important predictors, we suggest using the adaptive lasso method which is computationally efficient. Under some regularity conditions, the adaptive lasso method enjoys the oracle property in a general class of single-index models. In addition, the resulting estimation is shown to be asymptotically normal, which enables us to construct a confidence region for the estimated direction. The asymptotic results are augmented through comprehensive simulations, and illustrated by an analysis of air pollution data.
Starting Page	1277
Ending Page	1293
Page Count	17
File Format	PDF
ISSN	00203157
Journal	Annals of the Institute of Statistical Mathematics
Volume Number	63
Issue Number	6
e-ISSN	15729052
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-03-31
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Adaptive lasso Dimension reduction Oracle Sliced inverse regression Sparsity Statistics for Business/Economics/Mathematical Finance/Insurance Statistics
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability

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