Asymptotic Distribution of the Empirical Cumulative Distribution Function Predictor under Nonstationarity
In this paper, we establish a functional central limit theorem for the empirical predictor of a spatial cumulative distribution function for a random field with a nonstationary mean structure. The type of spatial asymptotic framework used here is somewhat nonstandard; it is a mixture of the so called “infill” and “increasing domain” asymptotic structures. The choice of the appropriate scaling sequence for the empirical predictor depends on certain characteristics of the spatial sampling design generating the sampling sites. A precise description of this dependence is given. The results obtained here extend a similar result of (1999) who considered only the stationary case.
KeywordsGaussian Process Weak Convergence Stationary Case Asymptotic Distribution Sampling Region
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