Article contents
A bootstrap algorithm for the isotropic random sphere
Published online by Cambridge University Press: 01 July 2016
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.
- Type
- Stochastic Geometry and Statistical Applications
- Information
- Copyright
- Copyright © Applied Probability Trust 1995
Footnotes
This research was partially supported by NSF grant DMS-94.04130.
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