We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
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.
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 (1993)) 
on the sphere, define 
to be a realization of the random process and 
to be the cardinality of 
. Without specifying the dependence structure of 
nor the marginal distribution of the 
, conditions for asymptotic normality of the standardized sample mean, 
, are given. The conditions on 
and 
are motivated by the ideas and results for dependent stationary sequences.
