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math.PR2026
Block-hierarchical covariance decompositions for finite-block additive functionals
Abbas Alhakim
We study additive functionals of stationary Markov chains whose observables depend on a fixed finite block of consecutive states. Such block observables arise naturally in sliding-…
math.ST2026
Overlapping window tests for correlation and trend
Abbas Alhakim
We develop a general framework for constructing and analyzing overlapping sliding-window statistics for dependence and trend detection. For a fixed window size, the overlapping blo…