## Electronic Journal of Statistics

### SiAM: A hybrid of single index models and additive models

#### 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.

#### Article information

Source
Electron. J. Statist., Volume 11, Number 1 (2017), 2397-2423.

Dates
First available in Project Euclid: 29 May 2017

https://projecteuclid.org/euclid.ejs/1496044838

Digital Object Identifier
doi:10.1214/17-EJS1291

Mathematical Reviews number (MathSciNet)
MR3656496

Zentralblatt MATH identifier
1364.62096

#### Citation

Ma, Shujie; Lian, Heng; Liang, Hua; Carroll, Raymond J. SiAM: A hybrid of single index models and additive models. Electron. J. Statist. 11 (2017), no. 1, 2397--2423. doi:10.1214/17-EJS1291. https://projecteuclid.org/euclid.ejs/1496044838

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