Cheng, B. and Tong, H.W and Bhansali, R.J and Robinson, P.M and Kleczkowski, A. (1994) Orthogonal Projection, Embedding Dimension and Sample-Size in Chaotic time-Series From a Statistical Perspective. Philosophical Transactions of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 348 (1688). pp. 325-341. ISSN 0962-8428.
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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.
|Subjects:||Q Science > Q Science (General)|
|Depositing User:||P. Ogbuji|
|Date Deposited:||02 Jul 2009 18:34|
|Last Modified:||02 Jul 2009 18:34|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/20439 (The current URI for this page, for reference purposes)|
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