Unconditional bases are optimal bases for data compression and for statistical estimation (Q1317208)

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.