Resampling: Consistency of substitution estimators
成果类型：
Article
署名作者：
Putter, H; vanZwet, WR
署名单位：
Leiden University; Leiden University - Excl LUMC; University of North Carolina; University of North Carolina Chapel Hill
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
发表日期：
1996
页码：
2297-2318
关键词：
摘要：
On the basis of N i.i.d. random variables with a common unknown distribution P we wish to estimate a functional tau(N)(P) An obvious and very general approach to this problem is to find an estimator (P) over cap(N) of P first, and then construct a so-called substitution estimator tau(N)((P) over cap(N)) of tau(N)(P). In this paper we investigate how to choose the estimator (P) over cap(N) so that the substitution estimator tau(N)((P) over cap(N)) Will be consistent. Although our setup covers a broad class of estimation problems, the main substitution estimator we have in mind is a general version of the bootstrap where resampling is done from an estimated distribution (P) over cap(N). We do not focus in advance on a particular estimator (P) over cap(N), such as, for example, the empirical distribution, but try to indicate which resampling distribution should be used in a particular situation. The conclusion that we draw from the results and the examples in this paper is that the bootstrap is an exceptionally flexible method which comes into its own when full use is made of its flexibility. However, the choice of a good bootstrap method in a particular case requires rather precise information about the structure of the problem at hand. Unfortunately, this may not always be available.