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Regularization and variable selection in Heckman selection model

Ogundimu, Emmanuel O.

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Sample selection arises when the outcome of interest is partially observed in a study. A common challenge is the requirement for exclusion restrictions. That is, some of the covariates affecting missingness mechanism do not affect the outcome. The drive to establish this requirement often leads to the inclusion of irrelevant variables in the model. A suboptimal solution is the use of classical variable selection criteria such as AIC and BIC, and traditional variable selection procedures such as stepwise selection. These methods are unstable when there is limited expert knowledge about the variables to include in the model. To address this, we propose the use of adaptive Lasso for variable selection and parameter estimation in both the selection and outcome submodels simultaneously in the absence of exclusion restrictions. By using the maximum likelihood estimator of the sample selection model, we constructed a loss function similar to the least squares regression problem up to a constant, and minimized its penalized version using an efficient algorithm. We show that the estimator, with proper choice of regularization parameter, is consistent and possesses the oracle properties. The method is compared to Lasso and adaptively weighted L1 penalized Two-step method. We applied the methods to the well-known Ambulatory Expenditure Data


Ogundimu, E. O. (2022). Regularization and variable selection in Heckman selection model. Statistical Papers, 63(2), 421-439.

Journal Article Type Article
Acceptance Date Jun 11, 2021
Online Publication Date Jun 16, 2021
Publication Date 2022-04
Deposit Date Jun 18, 2021
Publicly Available Date Aug 6, 2021
Journal Statistical Papers
Print ISSN 0932-5026
Electronic ISSN 1613-9798
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 63
Issue 2
Pages 421-439
Public URL


Published Journal Article (Advance online version) (337 Kb)

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Advance online version Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit

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