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Bayesian multivariate quantile regression using Dependent Dirichlet Process prior

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  • Bhattacharya, Indrabati
  • Ghosal, Subhashis

Abstract

In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The proposed approach involves modeling of related conditional distributions of a response vector given the covariates using a Dependent Dirichlet Process (DDP) prior. The DDP is used to introduce dependence across covariates. The flexible covariate-dependent mixture of multivariate Gaussian kernels gives rise to an induced posterior for the desired multivariate quantile. For posterior computations, we use a truncated stick-breaking representation of the DDP, and use a block Gibbs sampler for estimating the model parameters. We illustrate our method with simulation studies, and a data containing blood pressures of 40 women. Finally, we provide a theoretical justification for the proposed method through posterior consistency and support properties of the prior.

Suggested Citation

  • Bhattacharya, Indrabati & Ghosal, Subhashis, 2021. "Bayesian multivariate quantile regression using Dependent Dirichlet Process prior," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:jmvana:v:185:y:2021:i:c:s0047259x21000415
    DOI: 10.1016/j.jmva.2021.104763
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    2. Park, Seyoung & Kim, Hyunjin & Lee, Eun Ryung, 2023. "Regional quantile regression for multiple responses," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).

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