ORTHOGONAL PROJECTION, EMBEDDING DIMENSION AND SAMPLE-SIZE IN CHAOTIC TIME-SERIES FROM A STATISTICAL PERSPECTIVE

被引：16

作者：

CHENG, B

TONG, H

BHANSALI, RJ

ROBINSON, PM

KLECZKOWSKI, A

机构：

来源：

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 1994年 / 348卷 / 1688期

关键词：

D O I：

10.1098/rsta.1994.0094

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

By studying systematically the orthogonal projections, in a particular sense associated with a (random) time series admitting a possibly chaotic skeleton and in a sequence of suitably defined L(2)-spaces, we describe a geometric characterisation of the notion of embedding dimension within a statistical framework. The question of sample size requirement in the statistical estimation of the said dimension is addressed heuristically, ending with a pleasant surprise: the curse of dimensionality may be lifted except in the excessively stringent cases.

引用

页码：325 / 341

页数：17

共 29 条

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