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Variable Selection in Kernel Regression Using Measurement Error Selection Likelihoods

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  • Kyle R. White
  • Leonard A. Stefanski
  • Yichao Wu

Abstract

This article develops a nonparametric shrinkage and selection estimator via the measurement error selection likelihood approach recently proposed by Stefanski, Wu, and White. The measurement error kernel regression operator (MEKRO) has the same form as the Nadaraya–Watson kernel estimator, but optimizes a measurement error model selection likelihood to estimate the kernel bandwidths. Much like LASSO or COSSO solution paths, MEKRO results in solution paths depending on a tuning parameter that controls shrinkage and selection via a bound on the harmonic mean of the pseudo-measurement error standard deviations. We use small-sample-corrected AIC to select the tuning parameter. Large-sample properties of MEKRO are studied and small-sample properties are explored via Monte Carlo experiments and applications to data. Supplementary materials for this article are available online.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:520:p:1587-1597
    DOI: 10.1080/01621459.2016.1222287
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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. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
    3. 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.
    4. Clifford M. Hurvich & Jeffrey S. Simonoff & Chih‐Ling Tsai, 1998. "Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 271-293.
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