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Variable Selection in Nonparametric Classification Via Measurement Error Model Selection Likelihoods

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  • L. A. Stefanski
  • Yichao Wu
  • Kyle White

Abstract

Using the relationships among ridge regression, LASSO estimation, and measurement error attenuation as motivation, a new measurement-error-model-based approach to variable selection is developed. After describing the approach in the familiar context of linear regression, we apply it to the problem of variable selection in nonparametric classification, resulting in a new kernel-based classifier with LASSO-like shrinkage and variable-selection properties. Finite-sample performance of the new classification method is studied via simulation and real data examples, and consistency of the method is studied theoretically. Supplementary materials for the article are available online.

Suggested Citation

  • L. A. Stefanski & Yichao Wu & Kyle White, 2014. "Variable Selection in Nonparametric Classification Via Measurement Error Model Selection Likelihoods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 574-589, June.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:506:p:574-589
    DOI: 10.1080/01621459.2013.858630
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    References listed on IDEAS

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    1. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
    2. Daniela M. Witten & Robert Tibshirani, 2009. "Covariance‐regularized regression and classification for high dimensional problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 615-636, June.
    3. 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.
    4. Qing Mai & Hui Zou & Ming Yuan, 2012. "A direct approach to sparse discriminant analysis in ultra-high dimensions," Biometrika, Biometrika Trust, vol. 99(1), pages 29-42.
    5. Hall, Peter & Titterington, D. M. & Xue, Jing-Hao, 2009. "Median-Based Classifiers for High-Dimensional Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1597-1608.
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    Cited by:

    1. Hang Yu & Yuanjia Wang & Donglin Zeng, 2023. "A general framework of nonparametric feature selection in high‐dimensional data," Biometrics, The International Biometric Society, vol. 79(2), pages 951-963, June.
    2. Doksum, Kjell A. & Jiang, Jiancheng & Sun, Bo & Wang, Shuzhen, 2017. "Nearest neighbor estimates of regression," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 64-74.
    3. Kyle R. White & Leonard A. Stefanski & Yichao Wu, 2017. "Variable Selection in Kernel Regression Using Measurement Error Selection Likelihoods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1587-1597, October.

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