1 results
A bootstrap algorithm for the isotropic random sphere
- Part of
-
- Journal:
- Advances in Applied Probability / Volume 27 / Issue 3 / September 1995
- Published online by Cambridge University Press:
- 01 July 2016, pp. 627-641
- Print publication:
- September 1995
-
- Article
- Export citation
-
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.
be a real-valued, homogeneous, and isotropic random field indexed in 
. When restricted to those indices 
with 
, the Euclidean length of 
, equal to 
resides on the surface of a sphere of radius 
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.