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Variable selection in high-dimensional double generalized linear models

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  • Dengke Xu
  • Zhongzhan Zhang
  • Liucang Wu

Abstract

In this paper we are concerned with the problems of variable selection and estimation in double generalized linear models in which both the mean and the dispersion are allowed to depend on explanatory variables. We propose a maximum penalized pseudo-likelihood method when the number of parameters diverges with the sample size. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and asymptotic properties of the resulting estimators are established. We also carry out simulation studies and a real data analysis to assess the finite sample performance of the proposed variable selection procedure, showing that the proposed variable selection method works satisfactorily. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Dengke Xu & Zhongzhan Zhang & Liucang Wu, 2014. "Variable selection in high-dimensional double generalized linear models," Statistical Papers, Springer, vol. 55(2), pages 327-347, May.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:2:p:327-347
    DOI: 10.1007/s00362-012-0481-y
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    References listed on IDEAS

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    Cited by:

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    2. Xiaolin Chen & Xiaojing Chen & Yi Liu, 2019. "A note on quantile feature screening via distance correlation," Statistical Papers, Springer, vol. 60(5), pages 1741-1762, October.
    3. Heewon Park & Sadanori Konishi, 2017. "Principal component selection via adaptive regularization method and generalized information criterion," Statistical Papers, Springer, vol. 58(1), pages 147-160, March.
    4. Jun Lu & Lu Lin, 2020. "Model-free conditional screening via conditional distance correlation," Statistical Papers, Springer, vol. 61(1), pages 225-244, February.
    5. Hu Yang & Huilan Liu, 2016. "Penalized weighted composite quantile estimators with missing covariates," Statistical Papers, Springer, vol. 57(1), pages 69-88, March.
    6. 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.
    7. Shaomin Li & Haoyu Wei & Xiaoyu Lei, 2022. "Heterogeneous Overdispersed Count Data Regressions via Double-Penalized Estimations," Mathematics, MDPI, vol. 10(10), pages 1-25, May.

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