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- W3122445105 abstract "We derive bounds on the scope for a confidence band to adapt to the unknown regularity of a non-parametric function that is observed with noise, such as a regression function or density, under the self-similarity condition proposed by Gine and Nickl (2010). We find that adaptation can only be achieved up to a term that depends on the choice of the constant used to define self-similarity, and that this term becomes arbitrarily large for conservative choices of the self-similarity constant. We construct a confidence band that achieves this bound, up to a constant term that does not depend on the self-similarity constant. Our results suggest that care must be taken in choosing and interpreting the constant that defines self-similarity, since the dependence of adaptive confidence bands on this constant cannot be made to disappear asymptotically." @default.
- W3122445105 created "2021-02-01" @default.
- W3122445105 creator A5085709680 @default.
- W3122445105 date "2018-01-01" @default.
- W3122445105 modified "2023-09-26" @default.
- W3122445105 title "Adaptation Bounds for Confidence Bands under Self-Similarity" @default.
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- W3122445105 doi "https://doi.org/10.2139/ssrn.3272203" @default.
- W3122445105 hasPublicationYear "2018" @default.
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