Estimating dimension from small samples (Q1335315)

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.