## 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.

### MSC:

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