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arXiv · 2007.00797

Bayesian Multivariate Quantile Regression Using Dependent Dirichlet Process Prior

Indrabati Bhattacharya·Subhashis Ghosal
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Abstract

In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The collection of related conditional distributions of a response vector Y given a univariate covariate X is modeled using a Dependent Dirichlet Process (DDP) prior. The DDP is used to introduce dependence across x. As the realizations from a Dirichlet process prior are almost surely discrete, we need to convolve it with a kernel. To model the error distribution as flexibly as possible, we use a countable mixture of multidimensional normal distributions as our kernel. For posterior computations, we use a truncated stick-breaking representation of the DDP. This approximation enables us to deal with only a finitely number of parameters. We use a Block Gibbs sampler for estimating the model parameters. We illustrate our method with simulation studies and real data applications. Finally, we provide a theoretical justification for the proposed method through posterior consistency. Our proposed procedure is new even when the response is univariate.

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Indrabati Bhattacharya, Subhashis Ghosal. 2020-07-01. Bayesian Multivariate Quantile Regression Using Dependent Dirichlet Process Prior. https://arxiv.org/abs/2007.00797

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