Variable selection in parametric and semiparametric models

Since the proposal of the least absolute shrinkage and selection operator (LASSO) (Tibshirani, 1996) and the smoothly clipped absolute deviation (SCAD) method (Fan and Li, 2001), there have been extensive developments on model selection based on penalized log-likelihood and the computational issues...

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Main Author: Lin, Bingqing
Other Authors: School of Physical and Mathematical Sciences
Format: Theses and Dissertations
Language:English
Published: 2014
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Online Access:http://hdl.handle.net/10356/55280
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-552802023-02-28T23:57:35Z Variable selection in parametric and semiparametric models Lin, Bingqing School of Physical and Mathematical Sciences Pang Zhen DRNTU::Science::Mathematics::Statistics Since the proposal of the least absolute shrinkage and selection operator (LASSO) (Tibshirani, 1996) and the smoothly clipped absolute deviation (SCAD) method (Fan and Li, 2001), there have been extensive developments on model selection based on penalized log-likelihood and the computational issues of solving these problems in linear models. There are relatively less papers discussing model selection problems in some special but important parametric and semiparametric models, such as linear mixed-effects model, partially varying-coefficient single-index model and single-index-coefficient regression model. We propose a two-stage model selection procedure for the linear mixed-effects model. The procedure consists of two steps: First, penalized restricted log-likelihood is used to select the random effects, and this is done by adopting a Newton-type algorithm. Next, the penalized log-likelihood is used to select the fixed effects via pathwise coordinate optimization to improve the computation efficiency. For the partially varying-coefficient single-index model, we propose a class of efficient penalized estimating equations, which combine the smoothly clipped absolute deviation (SCAD) penalty and a stepwise estimation method. We propose a new procedure for model structure determination for the single-index-coefficient regression models; that is, the penalized estimating equations (PEE) for variable selection that combines the "delete-one-component" method and the smoothly clipped absolute deviation penalty. The proposed PEE method can simultaneously identify significant variables of the index and estimate the nonzero coefficients of the index parameters. We further study a hypothesis test procedure for nonparametric index-coefficient functions. Monte Carlo simulation studies are conducted to assess the finite sample performance of the proposed methods. And real-life examples are analyzed using the proposed methods as an illustration. ​Doctor of Philosophy (SPMS) 2014-01-07T08:46:59Z 2014-01-07T08:46:59Z 2014 2014 Thesis Lin, B. (2014). Variable selection in parametric and semiparametric models. Doctoral thesis, Nanyang Technological University, Singapore. http://hdl.handle.net/10356/55280 en 125 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Mathematics::Statistics
spellingShingle DRNTU::Science::Mathematics::Statistics
Lin, Bingqing
Variable selection in parametric and semiparametric models
description Since the proposal of the least absolute shrinkage and selection operator (LASSO) (Tibshirani, 1996) and the smoothly clipped absolute deviation (SCAD) method (Fan and Li, 2001), there have been extensive developments on model selection based on penalized log-likelihood and the computational issues of solving these problems in linear models. There are relatively less papers discussing model selection problems in some special but important parametric and semiparametric models, such as linear mixed-effects model, partially varying-coefficient single-index model and single-index-coefficient regression model. We propose a two-stage model selection procedure for the linear mixed-effects model. The procedure consists of two steps: First, penalized restricted log-likelihood is used to select the random effects, and this is done by adopting a Newton-type algorithm. Next, the penalized log-likelihood is used to select the fixed effects via pathwise coordinate optimization to improve the computation efficiency. For the partially varying-coefficient single-index model, we propose a class of efficient penalized estimating equations, which combine the smoothly clipped absolute deviation (SCAD) penalty and a stepwise estimation method. We propose a new procedure for model structure determination for the single-index-coefficient regression models; that is, the penalized estimating equations (PEE) for variable selection that combines the "delete-one-component" method and the smoothly clipped absolute deviation penalty. The proposed PEE method can simultaneously identify significant variables of the index and estimate the nonzero coefficients of the index parameters. We further study a hypothesis test procedure for nonparametric index-coefficient functions. Monte Carlo simulation studies are conducted to assess the finite sample performance of the proposed methods. And real-life examples are analyzed using the proposed methods as an illustration.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Lin, Bingqing
format Theses and Dissertations
author Lin, Bingqing
author_sort Lin, Bingqing
title Variable selection in parametric and semiparametric models
title_short Variable selection in parametric and semiparametric models
title_full Variable selection in parametric and semiparametric models
title_fullStr Variable selection in parametric and semiparametric models
title_full_unstemmed Variable selection in parametric and semiparametric models
title_sort variable selection in parametric and semiparametric models
publishDate 2014
url http://hdl.handle.net/10356/55280
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