MINIMAX BAYES ESTIMATION IN NONPARAMETRIC REGRESSION

被引：2
|
作者：
HECKMAN, NE [1 ]
WOODROOFE, M [1 ]
机构：
[1] UNIV MICHIGAN,DEPT STAT,ANN ARBOR,MI 48109
来源：
ANNALS OF STATISTICS | 1991年 / 19卷 / 04期
关键词：
MINIMAX ESTIMATES; BAYES ESTIMATES; NONPARAMETRIC REGRESSION; SMOOTHING;
D O I：
10.1214/aos/1176348383
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：
One observes n data points, (t(i), Y(i)), with the mean of Y(i), conditional on the regression function f, equal to f(t(i)). The prior distribution of the vector f = (f(t1),..., f(t(n)))t is unknown, but ties in a known class-OMEGA. An estimator, f, of f is found which minimizes the maximum E parallel-to f - f parallel-to 2. The maximum is taken over all priors in OMEGA and the minimum is taken over linear estimators of f. Asymptotic properties of the estimator are studied in the case that t(i) is one-dimensional and OMEGA is the set of priors for which f is smooth.
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页码：2003 / 2014
页数：12
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