A BOOTSTRAP ALGORITHM FOR THE ISOTROPIC RANDOM SPHERE

Let {X(?((p) over right arrow)} be a real-valued, homogeneous, and isotropic random field indexed in R(3). When restricted to those indices (p) over right arrow with \\(p) over right arrow\\ the Euclidean length of (p) over right arrow, equal to r (a positive constant), then the random field {X((p) over right arrow)} resides on the surface of a sphere of radius r. Using a modified stratified spherical sampling plan (Brown (1993a)) P on the sphere, define {X<((p)over) (right) (arrow)>:(p) over right arrow is an element of P} to be a realization of the random process and \P\ to be the cardinality of P. A bootstrap algorithm is presented and conditions for strong uniform consistency of the bootstrap cumulative distribution function of the standardized sample mean, \P\(-1/2)Sigma((p) over right arrow) (<is an) (element) (of)>) (P)(X((p) over right arrow)-E{X(<(p)over (arrow) (right) (arrow)>))}, are given. We illustrate the bootstrap algorithm with global land-area data.