NONPARAMETRIC REGRESSION UNDER QUALITATIVE SMOOTHNESS ASSUMPTIONS
成果类型：
Article
署名作者：
MAMMEN, E
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176348118
发表日期：
1991
页码：
741-759
关键词：
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.