ESTIMATING A SMOOTH MONOTONE REGRESSION FUNCTION

被引:172
作者
MAMMEN, E
机构
关键词
NONPARAMETRIC REGRESSION; ISOTONIC REGRESSION; KERNEL ESTIMATOR;
D O I
10.1214/aos/1176348117
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 problem of estimating a smooth monotone regression function m will be studied. We will consider the estimator m(SI) consisting of a smoothing step (application of a kernel estimator based on a kernel K) and of a isotonisation step (application of the pool adjacent violator algorithm). The estimator m(SI) will be compared with the estimator m(IS) where these two steps are interchanged. A higher order stochastic expansion of these estimators will be given which show that m(SI) and m(IS) are asymptotically first order equivalent and that m(IS) has a smaller mean squared error than m(SI) if and only if the kernel function of the kernel estimator is not too smooth.
引用
收藏
页码:724 / 740
页数:17
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