Estimating dimension from small samples
type: Item
instance of: scholarly article
title: Estimating dimension from small samples
zbMATH Open document ID: 0809.62019
DOI: 10.1016/0167-2789(94)90008-6
author: Kevin Judd
published in: Physica D
publication date: 1994-10-04T00:00:00Z
review text: A new algorithm to estimate the dimension of a measure from point samples has been described. It emphasizes that dimension need not be the same at all scales, that is, there need not be a ``scaling region''. When applied to sufficiently large samples of Gaussian measures, dimension estimates should be seen to converge to the measures' true dimensions. The algorithm is verified with this type of measures and is found to be reliable and have less demanding data requirements than conventional estimators. When one has additional knowledge of the convergence rate with cutoff, then extrapolation estimates can provide good estimates from very small samples.
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 646649
zbMATH Keywords: fractal dimension
zbMATH Keywords: new algorithm
zbMATH Keywords: point samples
zbMATH Keywords: Gaussian measures
zbMATH Keywords: dimension estimates
zbMATH Keywords: extrapolation estimates
MaRDI profile type: Publication
full work available at URL: 0167-2789(94)90008-6
OpenAlex ID: W1966017628
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description: scientific article; zbMATH DE number 646649