Unconditional bases are optimal bases for data compression and for statistical estimation (Q1317208)
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scientific article; zbMATH DE number 527694
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Unconditional bases are optimal bases for data compression and for statistical estimation |
scientific article; zbMATH DE number 527694 |
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Unconditional bases are optimal bases for data compression and for statistical estimation (English)
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13 March 1994
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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.
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orthogonal basis
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unconditional basis
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optimality property
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optimal recovery
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minimax data compression
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Mallat's heuristic principle
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