BOOTSTRAP ADAPTIVE ESTIMATION - THE TRIMMED-MEAN EXAMPLE

被引:21
作者
LEGER, C
ROMANO, JP
机构
[1] UNIV MONTREAL,DEPT INFORMAT & RECH OPERAT,MONTREAL H3C 3J7,QUEBEC,CANADA
[2] STANFORD UNIV,DEPT STAT,STANFORD,CA 94305
来源
CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE | 1990年 / 18卷 / 04期
关键词
ADAPTIVE ESTIMATION; BOOTSTRAP; CONFIDENCE LIMITS; TRIMMED MEAN;
D O I
10.2307/3315837.n
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 consider the problem of choosing among a class of possible estimators by selecting the estimator with the smallest bootstrap estimate of finite sample variance. This is an alternative to using cross-validation to choose an estimator adaptively. The problem of a confidence interval based on such an adaptive estimator is considered. We illustrate the ideas by applying the method to the problem of choosing the trimming proportion of an adaptive trimmed mean. It is shown that a bootstrap adaptive trimmed mean is asymptotically normal with an asymptotic variance equal to the smallest among trimmed means. The asymptotoc coverage probability of a bootstrap confidence interval based on such adaptive estimators is shown to have the nominal level. The intervals based on the asymptotic normality of the estimator share the same asymptotic result, but have poor small-sample properties compared to the bootstrap intervals. A small-sample simulation demonstrates that bootstrap adaptive trimmed means adapt themselves rather well even for samples of size 10.
引用
收藏
页码:297 / 314
页数:18
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