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Objective Bayesian group variable selection for linear model

Author

Listed:
  • Sang Gil Kang

    (Sangji University)

  • Woo Dong Lee

    (Daegu Haany University)

  • Yongku Kim

    (Kyungpook National University)

Abstract

Prediction variables of the regression model are grouped in many application problems. For example, a factor in an analysis of variance can have several levels or each original prediction variable in additive models can be expanded into different order polynomials or a set of basis functions. It is essential to select important groups and individual variables within the selected groups. In this study, we propose the objective Bayesian group and individual variable selections within the selected groups in the regression model to reduce the computational cost, even though the number of regression variables is large. Besides, we examine the consistency of the proposed group variable selection procedure. The proposed objective Bayesian approach is investigated using simulation and real data examples. The comparisons between the penalized regression approaches, Bayesian group lasso and the proposed method are presented.

Suggested Citation

  • Sang Gil Kang & Woo Dong Lee & Yongku Kim, 2022. "Objective Bayesian group variable selection for linear model," Computational Statistics, Springer, vol. 37(3), pages 1287-1310, July.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:3:d:10.1007_s00180-021-01160-w
    DOI: 10.1007/s00180-021-01160-w
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    References listed on IDEAS

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    1. Elías Moreno & F. Girón, 2008. "Comparison of Bayesian objective procedures for variable selection in linear regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(3), pages 472-490, November.
    2. F. Javier Girón & M. Lina Martínez & Elías Moreno & Francisco Torres, 2006. "Objective Testing Procedures in Linear Models: Calibration of the p‐values," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 765-784, December.
    3. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    4. Elías Moreno & F. Girón, 2008. "Comparison of Bayesian objective procedures for variable selection in linear regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(3), pages 491-492, November.
    5. Casella, George & Moreno, Elias, 2006. "Objective Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 157-167, March.
    6. Jian Huang & Shuange Ma & Huiliang Xie & Cun-Hui Zhang, 2009. "A group bridge approach for variable selection," Biometrika, Biometrika Trust, vol. 96(2), pages 339-355.
    7. 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.
    8. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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