Asymptotic distribution of the empirical spatial cumulative distribution function predictor and prediction bands based on a subsampling method
type: Item
instance of: scholarly article
title: Asymptotic distribution of the empirical spatial cumulative distribution function predictor and prediction bands based on a subsampling method
zbMATH Open document ID: 0951.62013
publication date: 1999-06-28T00:00:00Z
review text: The paper deals with the estimation of the spatial cumulative distribution function, via its empirical counterpart. A spatial cumulative function is a random distribution function that summarizes a random field over a given region. A functional limit theorem is established for the normalized predictor process. The asymptotic properties of the empirical spatial cumulative function are examined. It is shown that under uniform sampling design the rate of convergence of the estimate to the true distribution depends on the location of data-sites, determined by the sampling design. Illustrative examples are provided, those clearly describe the dependence. Finally a subsampling approach is described for integral based functionals of random fields. This approach allows for the construction of prediction bands for the spatial cumulative distribution function.
reviewed by: Dimitris Karlis
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 1309030
zbMATH Keywords: spatial cumulative distribution functions
zbMATH Keywords: subsampling
author: Soumendra N. Lahiri
MaRDI profile type: Publication
full work available at URL: s004400050221
OpenAlex ID: W2062677620
DOI: 10.1007/S004400050221
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1309030