Orthogonal Projection, Embedding Dimension and Sample Size in Chaotic Time Series from a Statistical Perspective

Citation

Cheng B, Tong H, Bhansali RJ, Robinson PM & Kleczkowski A (1994) Orthogonal Projection, Embedding Dimension and Sample Size in Chaotic Time Series from a Statistical Perspective. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 348 (1688), pp. 325-341. https://doi.org/10.1098/rsta.1994.0094

Abstract
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 $\scr{L}_{2}$-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.

Journal
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences: Volume 348, Issue 1688