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Group variable selection and estimation in the tobit censored response model


  • Liu, Xianhui
  • Wang, Zhanfeng
  • Wu, Yaohua


The tobit censored response model plays an important role in analyzing the dependent variable with a constraint at a pre-specified point such as 0, and is widely used in econometrics research. For this regression model, there are few studies on variable selection in a group manner. In this paper, we present a group variable selection and estimation method for predefined groups of variables. The proposed method selects variables significantly contributing to the regression model and presents consistent estimates of parameters in the selected groups. The asymptotic properties of the resulting estimates are similar to oracle properties. The performance of our method is evaluated with extensive simulation studies and a real example from a married women’s work hour study.

Suggested Citation

  • Liu, Xianhui & Wang, Zhanfeng & Wu, Yaohua, 2013. "Group variable selection and estimation in the tobit censored response model," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 80-89.
  • Handle: RePEc:eee:csdana:v:60:y:2013:i:c:p:80-89
    DOI: 10.1016/j.csda.2012.10.019

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    References listed on IDEAS

    1. Lukas Meier & Sara van de Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71.
    2. Mroz, Thomas A, 1987. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," Econometrica, Econometric Society, vol. 55(4), pages 765-799, July.
    3. Michelli Barros & Manuel Galea & Manuel González & Víctor Leiva, 2010. "Influence diagnostics in the tobit censored response model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 379-397, August.
    4. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    5. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    6. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    7. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67.
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    Cited by:

    1. Hussein Hashem & Veronica Vinciotti & Rahim Alhamzawi & Keming Yu, 2016. "Quantile regression with group lasso for classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 10(3), pages 375-390, September.
    2. Ding, Hao & Wang, Zhanfeng & Wu, Yaohua, 2017. "Tobit regression model with parameters of increasing dimensions," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 1-7.


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