Bootstrapping least distance estimator in the multivariate regression model

The most popular estimation methods in multivariate linear regression are the multivariate least squares estimation and the multivariate least absolute estimation. Each method repeats its univariate estimation method pp, the number of response variables, times. Although they are relatively easy to apply, they do not employ the relationship between response variables. This study considers the multivariate least distance estimator of Bai et al. (1990) that accounts for this relationship. We confirm its relative efficiency with respect to the multivariate least absolute estimator under the multivariate normal distribution and contaminated distribution. However, the asymptotic inference of the multivariate least distance estimator is shown to perform poorly in certain circumstances. We suggest the bootstrap method to infer the regression parameters and confirm its viability using Monte Carlo studies.