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A data version of the Gauss-Markov theorem and its application to adaptive subspace splitting

How does one adaptively split a measurement subspace into signal and orthogonal subspaces of reduced rank so that detectors, estimators, and quantizers may be adaptively designed from experimental data? The authors provide some answers to this question by decomposing experimental correlations into their Wishart distributed Schur complements and showing how these distributions may be used to identify subspaces.