Title

Model Selection in Validation Sampling Data: An Asymptotic Likelihood-based LASSO Approach

Publication Type

Journal Article

Publication Date

2011

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.

Keywords

Asymptotic likelihoodbased LASSO, LASSO, least squares approximation, validation sampling.

Discipline

Economics | Statistics and Probability

Research Areas

Econometrics

Publication

Statistica Sinica

Volume

21

First Page

659

Last Page

678

ISSN

1017-0405

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Additional URL

http://www3.stat.sinica.edu.tw/statistica/j21n2/J21N28/J21N28.html

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