SiAM: A Hybrid of Single Index Models and Additive Models. Academic Article

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.

authors

• Carroll, Raymond

published proceedings

• Electron J Stat

author list (cited authors)

• Ma, S., Lian, H., Liang, H., & Carroll, R. J.

citation count

• 3

complete list of authors

• Ma, Shujie||Lian, Heng||Liang, Hua||Carroll, Raymond J

publication date

• January 2017

publisher

• Institute of Mathematical Statistics  Publisher

published in

• Electronic Journal of Statistics  Journal

keywords

• Additive Models
• Global Inference
• Identifiability
• Misspecification
• Oracle Estimator
• Partially Linear Single Index Models
• Regression Spline
• Simultaneous Confidence Band

PubMed Central ID

• 29104711

Digital Object Identifier (DOI)

• 10.1214/17-EJS1291

start page

• 2397

end page

• 2423

volume

• 11

issue

• 1

URL

• http://dx.doi.org/10.1214/17-ejs1291