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Biometrika 2001 88(3):821-832; doi:10.1093/biomet/88.3.821
© 2001 by Biometrika Trust
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Single-index model selections

Prasad A.Naik1 and Chih-Ling Tsai1

1 Graduate School of Management, University of California, Davis, California 95616, U.S.Apanaik{at}ucdavis.edu cltsai{at}ucdavis.edu

We derive a new model selection criterion for single-index models, AICC, by minimising the expected Kullback–Leibler distance between the true and candidate models.The proposed criterion selects not only relevant variables but also the smoothing parameter for an unknown link function. Thus, it is a general selection criterion that provides a unified approach to model selection across both parametric and nonparametric functions. Monte Carlo studies demonstrate that AICC performs satisfactorily in most situations. We illustrate the practical use of AICC with an empirical example for modelling the hedonic price function for cars. In addition, we extend the applicability of AICC to partially linear and additive single-index models.

Key Words: Hedonic price function; Local polynomial regression; Sliced inverse regression; Smoothing parameter estimator; Variable selection

Received March 2000. Revised December 2000


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