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Bayesian quantile regression for partially linear single-index model with longitudinal data

Author

Listed:
  • Changsheng Liu

    (Henan University of Urban Construction)

  • Hanying Liang

    (Tongji University)

  • Yongmei Li

    (Tongji University
    Shanghai Institute of Pollution Control and Ecological Security)

Abstract

In this paper, we considered partially linear single-index quantile regression with longitudinal data. By using Bayesian techniques, quasi-posterior distributions of the linear and single-index parameters were constructed based on a quasi-likelihood function. Under suitable assumptions, we derived asymptotic normality of posterior estimators of the parameters, and established asymptotic relationship between the posterior estimators and their corresponding frequency estimators. Meanwhile, we used a stochastic search hierarchical model with spike-slab priors to perform variable selection and study consistency of the variable selection. Finite sample performance of the proposed methods was analyzed via simulation and real data too.

Suggested Citation

  • Changsheng Liu & Hanying Liang & Yongmei Li, 2025. "Bayesian quantile regression for partially linear single-index model with longitudinal data," Statistical Papers, Springer, vol. 66(1), pages 1-51, February.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:1:d:10.1007_s00362-024-01633-2
    DOI: 10.1007/s00362-024-01633-2
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