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.