An improved estimator of dimension and some comments on providing confidence intervals

Kevin Judd

Research output: Contribution to journalArticle

85 Citations (Scopus)

Abstract

An estimator of dimension is described that has many advantages over the conventional implementation of the Grassberger-Procaccia method. It can in some circumstances provide a confidence interval for the dimension estimate. For high dimension sets (greater than about 3.5) the dimension estimate has a bias which depends on the structure of the set. If one has suitable knowledge of the structure of the set it is possible to make a bias adjustment. Some numerical calculations are presented which indicate the largest error in the dimension estimate that can be expected. The problem of providing confidence intervals for dimension estimates in general is not solved completely, but we do take a step away from a meaningless number.
Original languageEnglish
Pages (from-to)216-228
JournalPhysica D
Volume56
DOIs
Publication statusPublished - 1992

Fingerprint

estimators
confidence
intervals
estimates
adjusting

Cite this

@article{836aa2c6606f4d77931feb4fb97b31ff,
title = "An improved estimator of dimension and some comments on providing confidence intervals",
abstract = "An estimator of dimension is described that has many advantages over the conventional implementation of the Grassberger-Procaccia method. It can in some circumstances provide a confidence interval for the dimension estimate. For high dimension sets (greater than about 3.5) the dimension estimate has a bias which depends on the structure of the set. If one has suitable knowledge of the structure of the set it is possible to make a bias adjustment. Some numerical calculations are presented which indicate the largest error in the dimension estimate that can be expected. The problem of providing confidence intervals for dimension estimates in general is not solved completely, but we do take a step away from a meaningless number.",
author = "Kevin Judd",
year = "1992",
doi = "10.1016/0167-2789(92)90025-I",
language = "English",
volume = "56",
pages = "216--228",
journal = "Physica D",
issn = "0167-2789",
publisher = "Pergamon",

}

An improved estimator of dimension and some comments on providing confidence intervals. / Judd, Kevin.

In: Physica D, Vol. 56, 1992, p. 216-228.

Research output: Contribution to journalArticle

TY - JOUR

T1 - An improved estimator of dimension and some comments on providing confidence intervals

AU - Judd, Kevin

PY - 1992

Y1 - 1992

N2 - An estimator of dimension is described that has many advantages over the conventional implementation of the Grassberger-Procaccia method. It can in some circumstances provide a confidence interval for the dimension estimate. For high dimension sets (greater than about 3.5) the dimension estimate has a bias which depends on the structure of the set. If one has suitable knowledge of the structure of the set it is possible to make a bias adjustment. Some numerical calculations are presented which indicate the largest error in the dimension estimate that can be expected. The problem of providing confidence intervals for dimension estimates in general is not solved completely, but we do take a step away from a meaningless number.

AB - An estimator of dimension is described that has many advantages over the conventional implementation of the Grassberger-Procaccia method. It can in some circumstances provide a confidence interval for the dimension estimate. For high dimension sets (greater than about 3.5) the dimension estimate has a bias which depends on the structure of the set. If one has suitable knowledge of the structure of the set it is possible to make a bias adjustment. Some numerical calculations are presented which indicate the largest error in the dimension estimate that can be expected. The problem of providing confidence intervals for dimension estimates in general is not solved completely, but we do take a step away from a meaningless number.

U2 - 10.1016/0167-2789(92)90025-I

DO - 10.1016/0167-2789(92)90025-I

M3 - Article

VL - 56

SP - 216

EP - 228

JO - Physica D

JF - Physica D

SN - 0167-2789

ER -