Abstract
A spatial cumulative distribution function F^∞ (say) is a random distribution function that provides a statistical summary of random field over a given region. This paper considers the empirical predictor of F^∞ based on a finite set of observations from a region in ℝd under a uniform sampling design. A functional central limit theorem is proved for the predictor as a random element of the space D[−∞, ∞]. A striking feature of the result is that the rate of convergence of the predictor to the predictand F^∞ depends on the location of the data-sites specified by the sampling design. A precise description of the dependence is given. Furthermore, a subsampling method is proposed for integral-based functionals of random fields, which is then used to construct large sample prediction bands for F^∞.
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Received: 14 July 1997 / Revised version: 2 June 1998
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Lahiri, S. Asymptotic distribution of the empirical spatial cumulative distribution function predictor and prediction bands based on a subsampling method. Probab Theory Relat Fields 114, 55–84 (1999). https://doi.org/10.1007/s004400050221
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DOI: https://doi.org/10.1007/s004400050221