Central double cross-validation for estimating parameters in regression models

The ridge regression, lasso, elastic net, forward stagewise regression and the least angle regression require a solution path and tuning parameter, λ, to estimate the coefficient vector. Therefore, it is crucial to find the ideal λ. Cross-validation (CV) is the most widely utilized method for choosi...

Full description

Saved in:

Bibliographic Details
Main Author:	Chye, Rou Shi
Format:	Thesis
Language:	English
Published:	2016
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/80959/2/ChyeRouShiMFS2016.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-utm-ep.80959
record_format	uketd_dc
spelling	my-utm-ep.809592019-07-24T00:13:24Z Central double cross-validation for estimating parameters in regression models 2016-07 Chye, Rou Shi QA Mathematics The ridge regression, lasso, elastic net, forward stagewise regression and the least angle regression require a solution path and tuning parameter, λ, to estimate the coefficient vector. Therefore, it is crucial to find the ideal λ. Cross-validation (CV) is the most widely utilized method for choosing the ideal tuning parameter from the solution path. CV is essentially the breaking down of the original sample into two parts. One part is used to develop the regression equation. The regression equation is then applied to the other part to evaluate the risk of every model. Consequently, the final model is the model with smallest estimated risk. However, CV does not provide consistent results because it has overfitting and underfitting effects during the model selection. In the present study, a new method for estimating parameter in best-subset regression called central double cross-validation (CDCV) is proposed. In this method, the CV is run twice with different number of folds. Therefore, CDCV maximizes the usage of available data, enhances the model selection performance and builds a new stable CV curve. The final model with an error of less than ?? standard error above the smallest CV error is chosen. The CDCV was compared to existing CV methods in determining the correct model via a simulation study with different sample size and correlation settings. Simulation study indicates that the proposed CDCV method has the highest percentage of obtaining the right model and the lowest Bayesian information criterion (BIC) value across multiple simulated study settings. The results showed that, CDCV has the ability to select the right model correctly and prevent the model from underfitting and overfitting. Therefore, CDCV is recommended as a good alternative to the existing methods in the simulation settings. 2016-07 Thesis http://eprints.utm.my/id/eprint/80959/ http://eprints.utm.my/id/eprint/80959/2/ChyeRouShiMFS2016.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:120286 masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Chye, Rou Shi Central double cross-validation for estimating parameters in regression models
description	The ridge regression, lasso, elastic net, forward stagewise regression and the least angle regression require a solution path and tuning parameter, λ, to estimate the coefficient vector. Therefore, it is crucial to find the ideal λ. Cross-validation (CV) is the most widely utilized method for choosing the ideal tuning parameter from the solution path. CV is essentially the breaking down of the original sample into two parts. One part is used to develop the regression equation. The regression equation is then applied to the other part to evaluate the risk of every model. Consequently, the final model is the model with smallest estimated risk. However, CV does not provide consistent results because it has overfitting and underfitting effects during the model selection. In the present study, a new method for estimating parameter in best-subset regression called central double cross-validation (CDCV) is proposed. In this method, the CV is run twice with different number of folds. Therefore, CDCV maximizes the usage of available data, enhances the model selection performance and builds a new stable CV curve. The final model with an error of less than ?? standard error above the smallest CV error is chosen. The CDCV was compared to existing CV methods in determining the correct model via a simulation study with different sample size and correlation settings. Simulation study indicates that the proposed CDCV method has the highest percentage of obtaining the right model and the lowest Bayesian information criterion (BIC) value across multiple simulated study settings. The results showed that, CDCV has the ability to select the right model correctly and prevent the model from underfitting and overfitting. Therefore, CDCV is recommended as a good alternative to the existing methods in the simulation settings.
format	Thesis
qualification_level	Master's degree
author	Chye, Rou Shi
author_facet	Chye, Rou Shi
author_sort	Chye, Rou Shi
title	Central double cross-validation for estimating parameters in regression models
title_short	Central double cross-validation for estimating parameters in regression models
title_full	Central double cross-validation for estimating parameters in regression models
title_fullStr	Central double cross-validation for estimating parameters in regression models
title_full_unstemmed	Central double cross-validation for estimating parameters in regression models
title_sort	central double cross-validation for estimating parameters in regression models
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2016
url	http://eprints.utm.my/id/eprint/80959/2/ChyeRouShiMFS2016.pdf
_version_	1747818284499075072

Central double cross-validation for estimating parameters in regression models

Similar Items