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Wilcoxon-type generalized Bayesian information criterion

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  • Lan Wang

Abstract

We develop a generalized Bayesian information criterion for regression model selection. The new criterion relaxes the usually strong distributional assumption associated with Schwarz's BIC by adopting a Wilcoxon-type dispersion function and appropriately adjusting the penalty term. We establish that the Wilcoxon-type generalized BIC preserves the consistency of Schwarz's BIC without the need to assume a parametric likelihood. We also show that it outperforms Schwarz's BIC with heavier-tailed data in the sense that asymptotically it can yield substantially smaller L-sub-2 risk. On the other hand, when the data are normally distributed, both criteria have similar L-sub-2 risk. The new criterion function is convex and can be conveniently computed using existing statistical software. Our proposal provides a flexible yet highly efficient alternative to Schwarz's BIC; at the same time, it broadens the scope of Wilcoxon inference, which has played a fundamental role in classical nonparametric analysis. Copyright 2009, Oxford University Press.

Suggested Citation

  • Lan Wang, 2009. "Wilcoxon-type generalized Bayesian information criterion," Biometrika, Biometrika Trust, vol. 96(1), pages 163-173.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:1:p:163-173
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    File URL: http://hdl.handle.net/10.1093/biomet/asn060
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    Cited by:

    1. Zou, Changliang & Chen, Xin, 2012. "On the consistency of coordinate-independent sparse estimation with BIC," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 248-255.
    2. Long Feng & Changliang Zou & Zhaojun Wang & Xianwu Wei & Bin Chen, 2015. "Robust spline-based variable selection in varying coefficient model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 85-118, January.
    3. Shao‐Hsuan Wang & Chin‐Tsang Chiang, 2020. "Concordance‐based estimation approaches for the optimal sufficient dimension reduction score," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 662-689, September.
    4. Yang, Hu & Guo, Chaohui & Lv, Jing, 2015. "SCAD penalized rank regression with a diverging number of parameters," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 321-333.

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