Estimating dimension from small samples

Kevin Judd

Research output: Contribution to journalArticle

55 Citations (Scopus)

Abstract

Details of a new algorithm to estimate the dimension of a measure from point samples are described. The new algorithm emphasizes that dimension need not be the same at all scales, that is, there need not be a ''scaling region.'' The algorithm is verified with Gaussian measures and is found to be reliable and have less demanding data requirements than conventional estimators. Using certain convergence properties of Gaussian measures, it is shown that good estimates can be made from very. small samples.
Original languageEnglish
Pages (from-to)421-429
JournalPhysica D
Volume71
DOIs
Publication statusPublished - 1994

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