Estimation of dimension for spatially distributed data and related limit theorems

C. D. Cutler and D. A. Dawson

Journal of Multivariate Analysis, 1989, vol. 28, issue 1, 115-148

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.

Keywords: Hausdorff; dimension; point; estimation; asymptotic; confidence; intervals; extreme; value; distribution; nearest; neighbor; statistic (search for similar items in EconPapers)
Date: 1989
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Citations: View citations in EconPapers (3)

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