NONPARAMETRIC REGRESSION UNDER QUALITATIVE SMOOTHNESS ASSUMPTIONS

被引：111

作者：

MAMMEN, E

机构：

来源：

ANNALS OF STATISTICS | 1991年 / 19卷 / 02期

关键词：

NONPARAMETRIC REGRESSION; SIMPLE QUALITATIVE CURVE CHARACTERISTICS; ISOTONIC AND CONCAVE REGRESSION; ESTIMATION OF THE SHAPE OF A FUNCTION;

D O I：

10.1214/aos/1176348118

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：

We propose a new nonparametric regression estimate. In contrast to the traditional approach of considering regression functions whose m th derivatives lie in a ball in the L-infinity or L2 norm, we consider the class of functions whose (m - 1)st derivative consists of at most k monotone pieces. For many applications this class seems more natural than the classical ones. The least squares estimator of this class is studied. It is shown that the speed of convergence is as fast as in the classical case.

引用

页码：741 / 759

页数：19

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