Key points are not available for this paper at this time.
The desire to make nonparametric regression robust leads to the problem of conditional median function estimation. Under appropriate regularity conditions, a sequence of local median estimators can be chosen to achieve the optimal rate of convergence n^-1/ (2+d) both pointwise and in the Lq (1 q <) norm restricted to a compact. It can also be chosen to achieve the optimal rate of convergence (n^-1 n) ^1/ (2+d) in the L^ norm restricted to a compact. These results also constitute an answer to an open question of Stone.
Young K. Truong (Thu,) studied this question.