SiAM: A hybrid of single index models and additive models

Ma, S; Lian, H; Liang, H; Carroll, RJ

SiAM: A hybrid of single index models and additive models

Ma, S Lian, H Liang, H Carroll, RJ

Permalink

Publication Type:: Journal Article
Citation:: Electronic Journal of Statistics, 2017, 11 (1), pp. 2397 - 2423
Issue Date:: 2017-01-01

Open Access

Copyright Clearance Process

Recently Added
In Progress
Open Access

This item is open access.

Adobe PDF

Download Published VersionAdobe PDF (385.94 kB)

View on publisher's site

View statistics

Full metadata record

Field	Value	Language
dc.contributor.author	Ma, S	en_US
dc.contributor.author	Lian, H	en_US
dc.contributor.author	Liang, H	en_US
dc.contributor.author	Carroll, RJ https://orcid.org/0000-0002-5465-9682	en_US
dc.date.issued	2017-01-01	en_US
dc.identifier.citation	Electronic Journal of Statistics, 2017, 11 (1), pp. 2397 - 2423	en_US
dc.identifier.issn	1935-7524	en_US
dc.identifier.uri	http://hdl.handle.net/10453/125190
dc.description.abstract	© 2017, Institute of Mathematical Statistics. All rights reserved. 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.	en_US
dc.relation.ispartof	Electronic Journal of Statistics	en_US
dc.relation.isbasedon	10.1214/17-EJS1291	en_US
dc.title	SiAM: A hybrid of single index models and additive models	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	11	en_US
utslib.for	0104 Statistics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	open_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	11	en_US

Abstract:

© 2017, Institute of Mathematical Statistics. All rights reserved. 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.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/125190