Keller G, Sporer R (1996)
Publication Type: Book chapter / Article in edited volumes
Publication year: 1996
Publisher: North-Holland, Amsterdam
Edited Volumes: Stochastic and spatial structures of dynamical systems (Amsterdam, 1995)
Series: Konink. Nederl. Akad. Wetensch. Verh. Afd. Natuurk. Eerste Reeks, 45
Book Volume: 45
Pages Range: 17--27
We discuss some statistical theory of the simultaneous estimation of correlation integrals from dynamical data with varying radii and embedding dimensions. Thereby we focus on the estimation of the covariance matrix of these estimators taking into account the finite sample size and the correlation time effects observed by Theiler [23]. As applications we discuss linear model statistics like linear regression estimates of correlation dimension and entropy and the detection of noise. 1 Introduction Let X 1 ; X 2 ; X 3 ; : : : be a real-valued stationary time series that is mixing in a sense to be made precise later. Typical examples would be a) independent identically distributed (i.i.d.) random observations, b) observation on a "chaotic" dynamical system, c) observations on a noisy system. In particular there may be some interesting dependence between consecutive observations that can be studied by looking at the distribution ¯ ` of blocks Y ` i := (X i ; : : : ; X i+`\Gamma1 ) 2 R ...
APA:
Keller, G., & Sporer, R. (1996). Remarks on the linear regression approach to dimension estimation. In S. J. van Strien, S. M. Verduyn Lunel (Eds.), Stochastic and spatial structures of dynamical systems (Amsterdam, 1995). (pp. 17--27). North-Holland, Amsterdam.
MLA:
Keller, Gerhard, and Ralph Sporer. "Remarks on the linear regression approach to dimension estimation." Stochastic and spatial structures of dynamical systems (Amsterdam, 1995). Ed. S. J. van Strien, S. M. Verduyn Lunel, North-Holland, Amsterdam, 1996. 17--27.
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