Abstract: Given a (J+1)-variate random sample {(X₁, Y₁),…, (X_n, Y_n)}, we consider the problem of estimating the conditional median functions of nonparametric regression by minimizing Σ|Y_i-g(X_i)|where g is based on tensor products of B-splines. If the true conditional median function is smooth up to order r, it is shown that the optimal global convergence rate, n^-r/(2r+J), is attained by the L₁-norm based estimators.

Key words: Least absolute deviation, nonparametric regresion, tensor product of Bsplines