Consistency of generalized maximum spacing estimates
1997 (English)Report (Other academic)
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 Kuliback-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 and Ekström (1997) (using simple spacings) and Ekström (1997) (using high order spacings) to obtain a class of estimation 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 and Hahn (1996) for the MSP method. In particular, it will be shown that GMSP methods give Ll consistent estimates in any family of distributions with unimodal densities, without any further conditions on the distributions.
Place, publisher, year, edition, pages
Umeå: Umeå universitet , 1997. , 15 p.
, Research report / Department of Mathematical Statistics, Umeå University, ISSN 1401-730X ; 1997:8
Estimation, Spacings, Consistency, Maximum spacing method, Unimodal density
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:umu:diva-85174OAI: oai:DiVA.org:umu-85174DiVA: diva2:691970