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Model selection in validation sampling: an asymptotic likelihood-based Lasso approach.
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Leng, Chenlei and Leung, Denis Heng-Yan (2011) Model selection in validation sampling: an asymptotic likelihood-based Lasso approach. Statistica Sinica, Volume 21 . 659-678 . ISSN 1017-0405.
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Official URL: http://www3.stat.sinica.edu.tw/statistica/j21n2/j2...
Abstract
We propose an asymptotic likelihood-based LASSO approach for model selection in regression analysis when data are subject to validation sampling. The method makes use of an initial estimator of the regression coefficients and their asymptotic covariance matrix to form an asymptotic likelihood. This ``working'' objective function facilitates the formulation of the LASSO and the implementation of a fast algorithm. Our method circumvents the need to use a likelihood set-up that requires full distributional assumptions about the data. We show that the resulting estimator is consistent in model selection and that the method has lower prediction errors than a model that uses only the validation sample. Furthermore, we show that this formulation gives an optimal estimator in a certain sense. Extensive simulation studies are conducted for the linear regression model, the generalized linear regression model, and the Cox model. Our simulation results support our claims. The method is further applied to a dataset to illustrate its practical use.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Statistica Sinica | ||||
Publisher: | Academia Sinica * Institute of Statistical Science | ||||
ISSN: | 1017-0405 | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Volume 21 | ||||
Number of Pages: | 19 | ||||
Page Range: | 659-678 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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