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

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.