On the asymptotic normality of the L2-error in partitioning regression estimation

被引:32
作者
Beirlant, J
Gyorfi, L
机构
[1] Tech Univ Budapest, Dept Math & Comp Sci, H-1521 Budapest, Hungary
[2] Catholic Univ Louvain, Dept Math, B-3000 Louvain, Belgium
关键词
nonparametric regression estimation; central limit theorem; partitioning estimate;
D O I
10.1016/S0378-3758(98)00008-1
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
The L-2-error of the partitioning regression estimator of a regression function m(x) = E(Y/X = x) using a cubic partition is shown to be asymptotically normal under the condition that X has a continuous density f of bounded support and Y satisfies some moment condition. (C) 1998 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:93 / 107
页数:15
相关论文
共 8 条
  • [1] ON THE ASYMPTOTIC NORMALITY OF THE L(1)-ERRORS AND L(2)-ERRORS IN HISTOGRAM DENSITY-ESTIMATION
    BEIRLANT, J
    GYORFI, L
    LUGOSI, G
    [J]. CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE, 1994, 22 (03): : 309 - 318
  • [2] BEIRLANT J, 1995, MATH METHODS STAT, V4, P1
  • [3] DEVROYE L, 1983, P 4 PANN S MATH STAT, P67
  • [4] Devroye L., 1996, A probabilistic theory of pattern recognition
  • [5] FAN J, 1996, MONOGRAPH STAT APPL, V66
  • [6] GYORFI L, 1991, NATO ADV SCI I C-MAT, V335, P329
  • [7] Korostelev A P., 1993, Minimax Theory of Image Reconstruction (Lecture Notes in Statistics vol 82)
  • [8] RAO CR, 1973, STAT INFERENCE ITS A