Linearity Identification for General Partial Linear Single-Index Models

Linearity Identification for General Partial Linear Single-Index Models

Partial linear models, a family of popular semiparametric models, provide us with an interpretable and flexible assumption for modelling complex data. One challenging question in partial linear models is the structure identification for the linear components and the nonlinear components, especially...

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Main Authors: Shaogao Lv, Luhong Wang
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2016/3537564
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spelling doaj-7eeda814120a4ca6b2c3e5f53ee0271b2020-11-24T21:00:23ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472016-01-01201610.1155/2016/35375643537564Linearity Identification for General Partial Linear Single-Index ModelsShaogao Lv0Luhong Wang1Center of Statistics, Southwestern University of Finance and Economics, Chengdu, ChinaCenter of Statistics, Southwestern University of Finance and Economics, Chengdu, ChinaPartial linear models, a family of popular semiparametric models, provide us with an interpretable and flexible assumption for modelling complex data. One challenging question in partial linear models is the structure identification for the linear components and the nonlinear components, especially for high dimensional data. This paper considers the structure identification problem in the general partial linear single-index models, where the link function is unknown. We propose two penalized methods based on a modern dimension reduction technique. Under certain regularity conditions, we show that the second estimator is able to identify the underlying true model structure correctly. The convergence rate of the new estimator is established as well.http://dx.doi.org/10.1155/2016/3537564
collection DOAJ
language English
format Article
sources DOAJ
author Shaogao Lv
Luhong Wang
spellingShingle Shaogao Lv
Luhong Wang
Linearity Identification for General Partial Linear Single-Index Models
Mathematical Problems in Engineering
author_facet Shaogao Lv
Luhong Wang
author_sort Shaogao Lv
title Linearity Identification for General Partial Linear Single-Index Models
title_short Linearity Identification for General Partial Linear Single-Index Models
title_full Linearity Identification for General Partial Linear Single-Index Models
title_fullStr Linearity Identification for General Partial Linear Single-Index Models
title_full_unstemmed Linearity Identification for General Partial Linear Single-Index Models
title_sort linearity identification for general partial linear single-index models
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2016-01-01
description Partial linear models, a family of popular semiparametric models, provide us with an interpretable and flexible assumption for modelling complex data. One challenging question in partial linear models is the structure identification for the linear components and the nonlinear components, especially for high dimensional data. This paper considers the structure identification problem in the general partial linear single-index models, where the link function is unknown. We propose two penalized methods based on a modern dimension reduction technique. Under certain regularity conditions, we show that the second estimator is able to identify the underlying true model structure correctly. The convergence rate of the new estimator is established as well.
url http://dx.doi.org/10.1155/2016/3537564
work_keys_str_mv AT shaogaolv linearityidentificationforgeneralpartiallinearsingleindexmodels
AT luhongwang linearityidentificationforgeneralpartiallinearsingleindexmodels
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