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On the asymptotic theory of subsampling (2001)
| Venue: | Statistica Sinica |
| Citations: | 7 - 1 self |
BibTeX
@ARTICLE{Politis01onthe,
author = {Dimitris N. Politis and Joseph P. Romano and Michael Wolf},
title = {On the asymptotic theory of subsampling},
journal = {Statistica Sinica},
year = {2001},
pages = {1105--1124}
}
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Abstract
Abstract: A general approach to constructing confidence intervals by subsampling was presented in Politis and Romano (1994). The crux of the method is recom-puting a statistic over subsamples of the data, and these recomputed values are used to build up an estimated sampling distribution. The method works under extremely weak conditions, it applies to independent, identically distributed (i.i.d.) observations as well as to dependent data situations, such as time series (possi-bly nonstationary), random fields, and marked point processes. In this article, we present some theorems showing: a new construction for confidence intervals that removes a previous condition, a general theorem showing the validity of subsam-pling for data-dependent choices of the block size, and a general theorem for the construction of hypothesis tests (not necessarily derived from a confidence interval construction). The arguments apply to both the i.i.d. setting and the dependent data case. Key words and phrases: Confidence intervals, data-dependent block size choice, hypothesis tests, large sample theory, resampling. 1.
Keyphrases
asymptotic theory confidence interval general theorem hypothesis test data-dependent block size choice large sample theory sampling distribution data situation point process block size dependent data case time series weak condition random field possi-bly nonstationary data-dependent choice previous condition key word general approach new construction confidence interval construction
