The maximum spacing estimation for multivariate observations

Abstract

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

Keywords

Estimation; spacings; consistency; multivariate observations

Published in

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

SLU Authors

• Teterukovsky, Alex

  • Department of Forest Economics, Swedish University of Agricultural Sciences
    

• Ranneby, Bo

  • Department of Forest Economics, Swedish University of Agricultural Sciences
    

UKÄ Subject classification

Probability Theory and Statistics


Publication identifier

DOI: https://doi.org/10.1016/j.jspi.2004.06.059

Permanent link to this page (URI)

https://res.slu.se/id/publ/6850