MODEL SELECTION IN VALIDATION SAMPLING: AN ASYMPTOTIC LIKELIHOOD-BASED LASSO APPROACH

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...

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Bibliographic Details
Published in:Statistica Sinica 2011-04, Vol.21 (2), p.659-678
Main Authors: Leng, Chenlei, Leung, Denis Heng-Yan
Format: Article
Language:English
Subjects:
Child psychopathology
Consistent estimators
Estimation methods
Estimators
Least squares
Linear regression
Modeling
Parents
Regression analysis
Simulations
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Summary: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.
ISSN:1017-0405
1996-8507
DOI:10.5705/ss.2011.029a