Asymptotic distribution of the empirical spatial cumulative distribution function predictor and prediction bands based on a subsampling method (Q1295875)

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.