Statistics and Its Interface

Volume 3 (2010)

Number 4

Dimension reduction and parameter estimation for additive index models

Pages: 493 – 499

DOI: https://dx.doi.org/10.4310/SII.2010.v3.n4.a7

Authors

Lingyan Ruan (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Ga., U.S.A.)

Ming Yuan (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Ga., U.S.A.)

Abstract

In this paper, we consider simultaneous model selection and estimation for the additive index model. The additive index model is a class of structured nonparametric models that can be expressed as additive models of a set of unknown linear transformation of the original predictor variables. We introduce a penalized least squares estimator and discuss how it can be efficiently computed in practice. Both theoretical and empirical properties of the estimate are presented to demonstrate its merits. Extensions to more general prediction framework are also discussed.

Keywords

additive model, index model, model selection, projection pursuit, smoothing splines

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Published 1 January 2010