数学物理学报(英文版) ›› 1996, Vol. 16 ›› Issue (S1): 57-69.
旋沛德, 郑忠国
Shi Peide, Zheng Zhongguo
摘要: Given a (J+1)-variate random sample {(X1, Y1),…, (Xn, Yn)}, we consider the problem of estimating the conditional median functions of nonparametric regression by minimizing Σ|Yi-g(Xi)|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.