TR multivariate conditional median estimation

An affine equivariant version of the nonparametric spatial conditional median (SCM) is constructed, using an adaptive transformation - retransformation (TR) procedure. The relative performance of SCM estimates, computed with and without applying the TR-procedure, are compared through simulations. Also included is the vector of coordinate conditional, kernel-based medians (VCCMs). The methodology is illustrated via an empirical data set. The simulations indicate that the TR-SCM estimator is more efficient than the SCM estimator for data generated from asymmetric contaminated trivariate normals. However, when the dimension of the covariates increases the efficiency of the TR-SCM estimator decreases. The TR-VCCM- and VCCM estimators lack efficiency, and consequently should not be used in practice.