Unconditional bases are optimal bases for data compression and for statistical estimation. (English) Zbl 0796.62083

The aim of this paper is to point out that an orthogonal basis of \(L^ 2\) which is also an unconditional basis of a functional space \(\mathcal F\) is an optimal basis for representing functions in \(\mathcal F\). The property of being an unconditional basis is an optimality property – optimality in three senses: for an optimal recovery problem, a minimax data compression problem, and a statistical estimation problem. As an application, the Mallat’s heuristic principle is formalized and proved.


62M99 Inference from stochastic processes
42C15 General harmonic expansions, frames
62M15 Inference from stochastic processes and spectral analysis
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