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Shrinkage tuning parameter selection with a diverging number of parameters

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  • Hansheng Wang
  • Bo Li
  • Chenlei Leng

Abstract

Contemporary statistical research frequently deals with problems involving a diverging number of parameters. For those problems, various shrinkage methods (e.g. the lasso and smoothly clipped absolute deviation) are found to be particularly useful for variable selection. Nevertheless, the desirable performances of those shrinkage methods heavily hinge on an appropriate selection of the tuning parameters. With a fixed predictor dimension, Wang and co-worker have demonstrated that the tuning parameters selected by a Bayesian information criterion type criterion can identify the true model consistently. In this work, similar results are further extended to the situation with a diverging number of parameters for both unpenalized and penalized estimators. Consequently, our theoretical results further enlarge not only the scope of applicabilityation criterion type criteria but also that of those shrinkage estimation methods. Copyright (c) 2008 Royal Statistical Society.

Suggested Citation

  • 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.
  • Handle: RePEc:bla:jorssb:v:71:y:2009:i:3:p:671-683
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    References listed on IDEAS

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    1. Peide Shi & Chih-Ling Tsai, 2002. "Regression model selection-a residual likelihood approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 237-252.
    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. Zhao, Meng & Kulasekera, K.B., 2006. "Consistent linear model selection," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 520-530, March.
    4. Yuhong Yang, 2005. "Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation," Biometrika, Biometrika Trust, vol. 92(4), pages 937-950, December.
    5. Hao Helen Zhang & Wenbin Lu, 2007. "Adaptive Lasso for Cox's proportional hazards model," Biometrika, Biometrika Trust, vol. 94(3), pages 691-703.
    6. Hansheng Wang & Guodong Li & Chih-Ling Tsai, 2007. "Regression coefficient and autoregressive order shrinkage and selection via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 63-78.
    7. Wang, Hansheng & Leng, Chenlei, 2007. "Unified LASSO Estimation by Least Squares Approximation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1039-1048, 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.
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