ON MULTIVARIATE QUANTILE REGRESSION

Biman Chakraborty

To detect the dependence on the covariates in the lower and upper tails of the response distribution, regression quantiles are very useful tools in linear model problems with univariate response. We consider here a notion of regression quantiles for problems with multivariate responses. The approach is based on minimizing a loss function equivalent to that in the case of univariate response. To construct an affine equivariant notion of multivariate quantiles, we have considered a transformation retransformation procedure based on `data-driven coordinate systems'. We indicate some algorithm to compute the proposed estimates and establish asymptotic normality for them. We also, suggest an adaptive procedure to select the optimal data-driven coordinate system. To illustrate our methodology, we analyzed an interesting data-set on blood pressures of a group of women and another one on the dependence of sales performances on creative test scores.