Abstract

General methods for the estimation of distributions can be derived from approximations of certain information measures. For example, both the maximum likelihood (ML) method and the maximum spacing (MSP) method can be obtained from approximations of the Kullback-Leibler information, The ideas behind the MSP method, whereby an estimation method for continuous univariate distributions is obtained from an approximation based on spacings of an information measure, were used by Ranneby & Ekstrom (1997) (using simple spacings) and Ekstrom (1997b) (using high order spacings) to obtain a class of methods, called generalized maximum spacing (GMSP) methods. In the present paper, GMSP methods will be shown to give consistent estimates under general conditions, comparable to those of Bahadur (1971) for the ML method, and those of Shao & Hahn (1999) for the MSP method. In particular, it will be proved that GMSP methods give L-1 consistent estimates in any family of distributions with unimodal densities, without any further conditions on the distributions.

Keywords

consistency; estimation; maximum spacing method spacings; unimodal density

Published in

Scandinavian Journal of Statistics
2001, Volume: 28, number: 2, pages: 343-354

SLU Authors

• Ekström, Magnus

  • Department of Forest Resource Management and Geomatics, Swedish University of Agricultural Sciences
    

UKÄ Subject classification

Probability Theory and Statistics


Publication identifier

DOI: https://doi.org/10.1111/1467-9469.00241

Permanent link to this page (URI)

https://res.slu.se/id/publ/100467