# Bayesian Estimation of Marginal Quantiles with Missing Data in a Multivariate Regression Framework

## TL;DR

This paper introduces a Bayesian method for estimating quantiles in multivariate regression with missing data, suitable for skewed and heavy-tailed data.

## Contribution

The novel contribution is a Bayesian multivariate regression framework for estimating marginal quantiles with missing data and skewed responses.

## Key findings

- The proposed Bayesian method effectively handles missing data in skewed response vectors.
- Simulation studies confirm the method's satisfactory performance in quantile estimation.
- The approach is successfully applied to real children's anthropometric data.

## Abstract

In this article, we propose and study a class of multivariate regression models that account for ignorable missing data in skewed, potentially heavy-tailed response vectors with positive components. It can be used to estimate the marginal quantiles of the response vectors based on a set of covariates, while considering the potential association among the components of the response vectors. We adopt an MCMC Bayesian approach to perform the posterior analysis via a monotone data augmentation algorithm for data imputation. The satisfactory performance of the posterior distributions and the handling of missing data in quantile estimation are verified through simulation studies. The procedures are illustrated using real children’s anthropometric data.