Asymptotic Distribution of the Empirical Cumulative Distribution Function Predictor under Nonstationarity

  • Jun Zhu
  • S. N. Lahiri
  • Noel Cressie
Part of the Lecture Notes in Statistics book series (LNS, volume 159)


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.


Gaussian Process Weak Convergence Stationary Case Asymptotic Distribution Sampling Region 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Jun Zhu
  • S. N. Lahiri
  • Noel Cressie

There are no affiliations available

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