Joint conditional quantiles inference of multivariate response regression model with VAR(q) error and its application in evaluating energy efficiency

This paper presents the joint parameters inference of conditional quantiles for a multivariate response linear regression model with a vector autoregressive (VAR) error using the expectation-maximization (EM) algorithm. Because the error follows a VAR model, the proposed approach accounts for the associations among multivariate responses and how the relationships between responses and explanatory variables vary across different quantiles of the marginal conditional distribution of responses. To facilitate likelihood-based inference using the EM algorithm, a multivariate asymmetric Laplace (MAL) distribution is forced on the independent errors of the model, thereby allowing the construction of an equivalently joint quantile model. Meanwhile, a location-scale mixture representation of the MAL distribution is employed to simplify the model’s working likelihood structure. Last, we present simulation studies and the analysis of real data for concerning on energy efficiency evaluation in order to illustrate the proposed modeling approach’s effectiveness.