Donoho, David L. Unconditional bases are optimal bases for data compression and for statistical estimation. (English) Zbl 0796.62083 Appl. Comput. Harmon. Anal. 1, No. 1, 100-115 (1993). 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. Reviewer: I.Křivý (Ostrava) Cited in 2 ReviewsCited in 69 Documents MSC: 62M99 Inference from stochastic processes 42C15 General harmonic expansions, frames 62M15 Inference from stochastic processes and spectral analysis Keywords:orthogonal basis; unconditional basis; optimality property; optimal recovery; minimax data compression; Mallat’s heuristic principle PDFBibTeX XMLCite \textit{D. L. Donoho}, Appl. Comput. Harmon. Anal. 1, No. 1, 100--115 (1993; Zbl 0796.62083) Full Text: DOI Link