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A bootstrap algorithm for the isotropic random sphere

Part of: Stochastic processes Nonparametric inference

Published online by Cambridge University Press:  01 July 2016

Jason J. Brown
Jason J. Brown*
Affiliation:
University of Missouri—Columbia
*
* Present address: 5825 Saddle Seat Drive, Raleigh, NC 27606, USA.
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Abstract

Let be a real-valued, homogeneous, and isotropic random field indexed in . When restricted to those indices with , the Euclidean length of , equal to r (a positive constant), then the random field resides on the surface of a sphere of radius r. Using a modified stratified spherical sampling plan (Brown (1993a)) on the sphere, define to be a realization of the random process and to be the cardinality of . A bootstrap algorithm is presented and conditions for strong uniform consistency of the bootstrap cumulative distribution function of the standardized sample mean, , are given. We illustrate the bootstrap algorithm with global land-area data.

Keywords

BOOTSTRAPSAMPLING PLANISOTROPIC RANDOM FIELDSPHERE

MSC classification

Primary: 62G09: Resampling methods
Secondary: 60G60: Random fields

Information

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 27 , Issue 3 , September 1995 , pp. 627 - 641
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

This research was partially supported by NSF grant DMS-94.04130.

References

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