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Bayesian estimation and variable selection for single index models

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  • Wang, Hai-Bin

Abstract

We develop a fully Bayesian method to analyze the single index models, including variable selection, the index vector estimation and the link function fitting with free-knot splines. The proposed method is implemented by means of the reversible jump Markov chain Monte Carlo technique. We treat the marginal posterior of all the unknown quantities except the spline coefficients and error variance as the target distribution to reduce the dimension of the parameters and to obtain a rapid algorithm. We design a new random walk Metropolis sampler to sample from the conditional posterior distribution of the index vector. The proposed method is verified by simulation studies, and is applied to analyze two real data sets.

Suggested Citation

  • Wang, Hai-Bin, 2009. "Bayesian estimation and variable selection for single index models," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2617-2627, May.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:7:p:2617-2627
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    References listed on IDEAS

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    1. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    2. Lindstrom, Mary J., 2002. "Bayesian estimation of free-knot splines using reversible jumps," Computational Statistics & Data Analysis, Elsevier, vol. 41(2), pages 255-269, December.
    3. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
    4. C. C. Holmes & B. K. Mallick, 2001. "Bayesian regression with multivariate linear splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 3-17.
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    Cited by:

    1. Wai-Yin Poon & Hai-Bin Wang, 2014. "Multivariate partially linear single-index models: Bayesian analysis," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 755-768, December.
    2. Jianbo Li & Yuan Li & Riquan Zhang, 2017. "B spline variable selection for the single index models," Statistical Papers, Springer, vol. 58(3), pages 691-706, September.
    3. Yazhao Lv & Riquan Zhang & Weihua Zhao & Jicai Liu, 2014. "Quantile regression and variable selection for the single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1565-1577, July.
    4. Hyung G. Park & Danni Wu & Eva Petkova & Thaddeus Tarpey & R. Todd Ogden, 2023. "Bayesian Index Models for Heterogeneous Treatment Effects on a Binary Outcome," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 397-418, July.
    5. Xiaohui Yuan & Xuefei Xiang & Xinran Zhang, 2023. "Bayesian composite quantile regression for the single-index model," PLOS ONE, Public Library of Science, vol. 18(5), pages 1-17, May.
    6. Rahul Ghosal & Arnab Maity, 2024. "Variable selection in function-on-scalar single-index model via the alternating direction method of multipliers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(1), pages 106-126, March.
    7. Yunquan Song & Hang Su & Minmin Zhan, 2024. "Local Walsh-average-based Estimation and Variable Selection for Spatial Single-index Autoregressive Models," Networks and Spatial Economics, Springer, vol. 24(2), pages 313-339, June.

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