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Estimation of dimension for spatially distributed data and related limit theorems

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  • Cutler, C. D.
  • Dawson, D. A.

Abstract

In this paper we investigate the dimensional structure of probability distributions on Euclidean space and characterize a class of regular distributions. We obtain a consistent estimator of dimension based on a nearest neighbor statistic and in addition obtain asymptotic confidence intervals for dimension in the case of regular distributions. Although many examples of point estimation of dimension have recently appeared in the literature on chaotic attractors in dynamical systems, questions of consistency and interval estimation have not previously been addressed systematically.

Suggested Citation

  • Cutler, C. D. & Dawson, D. A., 1989. "Estimation of dimension for spatially distributed data and related limit theorems," Journal of Multivariate Analysis, Elsevier, vol. 28(1), pages 115-148, January.
    • Handle: RePEc:eee:jmvana:v:28:y:1989:i:1:p:115-148
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    Cited by:

    1. Pötzelberger Klaus, 2003. "Estimating the dimension of factors of diffusion processes," Statistics & Risk Modeling, De Gruyter, vol. 21(2/2003), pages 171-184, February.
    2. Spodarev, Evgeny & Straka, Peter & Winter, Steffen, 2015. "Estimation of fractal dimension and fractal curvatures from digital images," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 134-152.
    3. Denker, Manfred & Min, Aleksey, 2008. "A central limit theorem for measurements on the logarithmic scale and its application to dimension estimates," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 665-683, April.

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