DimensionEstimation

Research topics

Dimension Estimation †

Abstract †

We present a new estimator of the distribution of pointwise dimensions of a probability measure. Our estimator seeks to approximate such measures by locally uniform measures, which we show are dense in a large class. We derive a probability density related to a locally uniform measure which allows estimation of its pointwise dimensions by a Bayesian method. We discuss our algorithm in detail and apply it to various data, including orbits of the classical H´enon map and a Chirikov standard map.

Presentation †

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MATLAB codes †

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Related papers †

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• PubSelected?PreprintPub2013MethodologicalImprovementDimensionEstimation Hidaka, S. & Kashyap, N. (2013). On the Estimation of Pointwise Dimension., eprint arXiv:1312.2298. (link) [Publications]