L_2-cross-validation最近邻中位数估计的渐近最优性

ASYMPTOTIC OPTIMALITY FOR L2-CROSS-VALIDATED NEAREST NEIGHBOR MEDIAN REGRESSION ESTIMARES

本文研究固定设计点模型的最近邻中位数估计的光滑参数的选择问题.在一定的正则性条件下得到了L2-cross-validation最近邻中位数估计的渐近最优性.同时还得到了最近邻中位数估计的弱Bahadur表示.

Nearest neighbor median estimators of an unknown regression function are investigated. The Bahadur representation of the estimator are given and the asymptotic optimality for L2- cross-validated nearest neighbor median estimator are established under the mild conditions.