A new estimator for information dimension with standard errors and confidence intervals
type: Item
instance of: scholarly article
title: A new estimator for information dimension with standard errors and confidence intervals
zbMATH Open document ID: 0934.62008
DOI: 10.1016/S0304-4149(97)00073-2
published in: Stochastic Processes and their Applications
publication date: 2000-03-01T00:00:00Z
review text: The problem how to estimate the information dimension \[ \lim _{r\rightarrow 0} (\log r)^{-1} \int \log \mu (\{u\in R^d:\|x-u\|\leq r\}) d\mu (x) \] of the probability measure \(\mu \) on \(X\subset R^d\), on the basis of a finite sample \(X_1,\ldots ,X_N\), of \(R^d\)-valued observations with distribution \(\mu \) is solved. The estimation algorithm is similar to the Grassberger-Procaccia algorithm for estimating the correlation dimension. Under mixing assumptions on the observations, the new estimator is asymptotically normal.
Mathematics Subject Classification ID: 62B10
Mathematics Subject Classification ID: 62M09
zbMATH DE Number: 1409141
zbMATH Keywords: information dimension
zbMATH Keywords: local dimension
zbMATH Keywords: smoothly trimmed spatial correlation integral
zbMATH Keywords: U-statistics
zbMATH Keywords: L-statistics
author: G. Keller
reviewed by: Lubomír Kubáček
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1409141