Statistical Applications of a Metric on Subspaces to Satellite Meteorology

In many large-dimensional multivariate problems, it is useful to reduce the number of variates. One method of reducing the number of dimensions is to project the original data onto a subspace. The statistical analysis is then carried out in this subspace. Principal-component regression is an example of such a technique. For these applications it is useful to have a measure of the distance between subspaces and to study the sampling stability of such subspaces. To solve these problems, we use a metric on subspaces and bootstrap techniques. The techniques are applied to seven-dimensional vectors of upwelling radiances from the current meteorological satellites. We study the subspaces spanned by the principal components based on a sample categorized by location and surface type.