Open Access
2017 SiAM: A hybrid of single index models and additive models
Shujie Ma, Heng Lian, Hua Liang, Raymond J. Carroll
Electron. J. Statist. 11(1): 2397-2423 (2017). DOI: 10.1214/17-EJS1291

Abstract

While popular, single index models and additive models have potential limitations, a fact that leads us to propose SiAM, a novel hybrid combination of these two models. We first address model identifiability under general assumptions. The result is of independent interest. We then develop an estimation procedure by using splines to approximate unknown functions and establish the asymptotic properties of the resulting estimators. Furthermore, we suggest a two-step procedure for establishing confidence bands for the nonparametric additive functions. This procedure enables us to make global inferences. Numerical experiments indicate that SiAM works well with finite sample sizes, and are especially robust to model structures. That is, when the model reduces to either single-index or additive scenario, the estimation and inference results are comparable to those based on the true model, while when the model is misspecified, the superiority of our method can be very great.

Citation

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Shujie Ma. Heng Lian. Hua Liang. Raymond J. Carroll. "SiAM: A hybrid of single index models and additive models." Electron. J. Statist. 11 (1) 2397 - 2423, 2017. https://doi.org/10.1214/17-EJS1291

Information

Received: 1 August 2016; Published: 2017
First available in Project Euclid: 29 May 2017

zbMATH: 1364.62096
MathSciNet: MR3656496
Digital Object Identifier: 10.1214/17-EJS1291

Subjects:
Primary: 62G08
Secondary: 62F12 , 62G20 , 62J02

Keywords: Additive models , global inference , Identifiability , misspecification , oracle estimator , partially linear single index models , regression spline , simultaneous confidence band

Vol.11 • No. 1 • 2017
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