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Research article - Peer-reviewed, 2005

The maximum spacing estimation for multivariate observations

Ranneby B, Jammalamadaka SR, Teterukovskiy A


For independently and identically distributed (i.i.d.) univariate observations a new estimation method, the maximum spacing (MSP) method, was defined in Ranneby (Scand. J. Statist. 11 (1984) 93) and independently by Cheng and Amin (J. Roy. Statist. Soc. B 45 (1983) 394). The idea behind the method, as described by Ranneby (Scand. J. Statist. 11 (1984) 93), is to approximate the Kullback-Leibler information so each contribution is bounded from above. In the present paper the MSP-method is extended to multivariate observations. Since we do not have any natural order relation in R-d when d > 1 the approach has to be modified. Essentially, there are two different approaches, the geometric or probabilistic counterpart to the univariate case. If we to each observation attach its Dirichlet cell, the geometrical correspondence is obtained. The probabilistic counterpart would be to use the nearest neighbor balls. This, as the random variable, giving the probability for the nearest neighbor ball, is distributed as the minimum of (n - 1) i.i.d. uniformly distributed variables on the interval (0, 1), regardless of the dimension d. Both approaches are discussed in the present paper. (C) 2004 Elsevier B.V. All rights reserved


Estimation; spacings; consistency; multivariate observations

Published in

Journal of Statistical Planning and Inference
2005, Volume: 129, number: 1-2, pages: 427-446

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    • UKÄ Subject classification

      Probability Theory and Statistics

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