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Variable selection and estimation in high-dimensional models

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  • Joel L. Horowitz

Abstract

Models with high-dimensional covariates arise frequently in economics and other fields. Often, only a few covariates have important effects on the dependent variable. When this happens, the model is said to be sparse. In applications, however, it is not known which covariates are important and which are not. This paper reviews methods for discriminating between important and unimportant covariates with particular attention given to methods that discriminate correctly with probability approaching 1 as the sample size increases. Methods are available for a wide variety of linear, nonlinear, semiparametric and nonparametric models. The performance of some of these methods in finite samples is illustrated through Monte Carlo simulations and an empirical example.

Suggested Citation

  • Joel L. Horowitz, 2015. "Variable selection and estimation in high-dimensional models," Canadian Journal of Economics, Canadian Economics Association, vol. 48(2), pages 389-407, May.
  • Handle: RePEc:cje:issued:v:48:y:2015:i:2:p:389-407
    DOI: 10.1111/caje.12130
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    References listed on IDEAS

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    1. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    2. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    4. Nicolai Meinshausen & Peter Bühlmann, 2010. "Stability selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 417-473, September.
    5. Kim, Yongdai & Choi, Hosik & Oh, Hee-Seok, 2008. "Smoothly Clipped Absolute Deviation on High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1665-1673.
    6. Wang, Tao & Xu, Pei-Rong & Zhu, Li-Xing, 2012. "Non-convex penalized estimation in high-dimensional models with single-index structure," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 221-235.
    7. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 663-690, September.
    8. 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.
    9. Sala-i-Martin, Xavier, 1997. "I Just Ran Two Million Regressions," American Economic Review, American Economic Association, vol. 87(2), pages 178-183, May.
    10. Heng Lian, 2012. "Variable selection in high-dimensional partly linear additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 825-839, December.
    11. Hansheng Wang & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683, June.
    12. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    13. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    14. Efang Kong & Yingcun Xia, 2007. "Variable selection for the single‐index model," Biometrika, Biometrika Trust, vol. 94(1), pages 217-229.
    15. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    16. Antoniadis A. & Fan J., 2001. "Regularization of Wavelet Approximations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 939-967, September.
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    Cited by:

    1. Horowitz, Joel L. & Nesheim, Lars, 2021. "Using penalized likelihood to select parameters in a random coefficients multinomial logit model," Journal of Econometrics, Elsevier, vol. 222(1), pages 44-55.
    2. Michael C. Knaus & Michael Lechner & Anthony Strittmatter, 2022. "Heterogeneous Employment Effects of Job Search Programs: A Machine Learning Approach," Journal of Human Resources, University of Wisconsin Press, vol. 57(2), pages 597-636.
    3. Adriano Zanin Zambom & Gregory J. Matthews, 2021. "Sure independence screening in the presence of missing data," Statistical Papers, Springer, vol. 62(2), pages 817-845, April.
    4. Joel L. Horowitz & Lars Nesheim, 2018. "Using penalized likelihood to select parameters in a random coefficients multinomial logit model," CeMMAP working papers CWP29/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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