Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress

Abstract

This paper proposes a maximum-likelihood approach to jointly estimate marginal conditional quantiles of multivariate response variables in a linear regression framework.We consider a slight reparameterization of the Multivariate Asymmetric Laplace distribution proposed by Kotz et al (2001) and exploit its location-scale mixture representation to implement a new EM algorithm for estimating model parameters. The idea is to extend the link between the Asymmetric Laplace distribution and the well-known univariate quantile regression model to a multivariate context, i.e. when a multivariate dependent variable is concerned. The approach accounts for association among multiple responses and study how the relationship between responses and explanatory variables can vary across different quantiles of the marginal conditional distribution of the responses. A penalized version of the EM algorithm is also presented to tackle the problem of variable selection. The validity of our approach is analyzed in a simulation study, where we also provide evidence on the efficiency gain of the proposed method compared to estimation obtained by separate univariate quantile regressions. A real data application is finally proposed to study the main determinants of financial distress in a sample of Italian firms.

M-Quantile Regression for Multivariate Longitudinal Data with an Application to the Millennium Cohort Study

“…(2001). In the quantile regression framework, the extension to multivariate responses has been dealt by Petrella and Raponi (2019). They account for the association among several responses while studying the effect of observed predictors on different quantiles of the marginal (univariate) conditional distribution of the responses.…”

Bayesian joint inference for multivariate quantile regression model with L$$_{1/2}$$ penalty

“…, σ p )). Petrella and Raponi (2019) proved that the j-th marginal distribution of Y i under the assumption of MAL distribution is a UAL distribution AL(β T τ j X i , τ j , σ j ) for j ∈ 1, . .…”

“…There is scattered literature for joint quantile inference of multivariate-response regression models. Recently, Petrella and Raponi (2019) extended the univariate linear quantile regression approach to a multivariate framework based on the multivariate asymmetric Laplace (MAL) distribution using EM algorithm. In this paper, we consider joint inference of the multivariate linear quantie regression models from a Bayesian point of view.…”

Housing Price Prediction Based on Multiple Linear Regression

“…On the other hand, the other method is called the backward method, in which we assume a complicated model first, and we then fit the model, trying to simplify it. Both methods could achieve the same goal for modeling the data appropriately, depending on the given situation and features of the data set [17].…”