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Large sample confidence regions based on subsamples under minimal assumptions. (English) Zbl 0828.62044
Summary: 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 C. F. J. Wu [ibid. 18, No. 3, 1438- 1452 (1990; Zbl 0705.62044)] 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 needs 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.

MSC:
62G15 Nonparametric tolerance and confidence regions
62G20 Asymptotic properties of nonparametric inference
62M40 Random fields; image analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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