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December, 1994 Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions
Dimitris N. Politis, Joseph P. Romano
Ann. Statist. 22(4): 2031-2050 (December, 1994). DOI: 10.1214/aos/1176325770


In this article, the construction of confidence regions by approximating the sampling distribution of some statistic is studied. The true sampling distribution is estimated by an appropriate normalization of the values of the statistic computed over subsamples of the data. In the i.i.d. context, the method has been studied by Wu in regular situations where the statistic is asymptotically normal. The goal of the present work is to prove the method yields asymptotically valid confidence regions under minimal conditions. Essentially, all that is required is that the statistic, suitably normalized, possesses a limit distribution under the true model. Unlike the bootstrap, the convergence to the limit distribution need not be uniform in any sense. The method is readily adapted to parameters of stationary time series or, more generally, homogeneous random fields. For example, an immediate application is the construction of a confidence interval for the spectral density function of a homogeneous random field.


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Dimitris N. Politis. Joseph P. Romano. "Large Sample Confidence Regions Based on Subsamples under Minimal Assumptions." Ann. Statist. 22 (4) 2031 - 2050, December, 1994.


Published: December, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0828.62044
MathSciNet: MR1329181
Digital Object Identifier: 10.1214/aos/1176325770

Primary: 60F99
Secondary: 62G99

Keywords: Approximate confidence limit , bootstrap , homogeneous random field , Jackknife histogram , stationary , time series

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.22 • No. 4 • December, 1994
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