Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Maximum spacing estimates based on different metrics
Department of Forest Resource Management and Geomatics Swedish University of Agricultural Sciences, Umeå, Sweden.
Umeå University, Faculty of Science and Technology, Mathematical statistics.
1997 (English)Report (Other academic)
Abstract [en]

The maximum spacing (MSP) method, introduced by Cheng and Amin (1983) and independently by Ranneby (1984), is a general method for estimating param­eters in univariate continuous distributions and is known to give consistent and asymptotically efficient estimates under general conditions. This method, which is closely related to the maximum likelihood (ML) method, can be derived from an approximation based on simple spacings of the Kullback-Leibler information. In the present paper, the ideas behind the MSP metod axe extended and a class of estimation methods is derived from approximations of certain information mea­sures, i.e. the ^-divergences introduced by Csiszâr (1963). We call these methods generalized maximum spacing (GMSP) methods, and it will be shown under gen­eral conditions that they give consistent estimates. GMSP methods have the advantage that they work also in situations where the ML method breaks down, e.g. due to an unbounded likelihood function. Other properties, such as asymp­totic normality and the behaviour of the estimates when the assigned model is only approximately true, will be discussed.[1]

[1] Research was supported by MISTRA, the Foundation for Strategic Environmental Research.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 1997. , 18 p.
Series
Research report / Department of Mathematical Statistics, Umeå University, ISSN 1401-730X ; 1997:5
Keyword [en]
Estimation, Spacings, Maximum spacing method, Consistency, ^-divergence
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-85171OAI: oai:DiVA.org:umu-85171DiVA: diva2:691955
Projects
digitalisering@umu
Available from: 2014-01-29 Created: 2014-01-29 Last updated: 2014-01-30Bibliographically approved
In thesis
1. Maximum spacing methods and limit theorems for statistics based on spacings
Open this publication in new window or tab >>Maximum spacing methods and limit theorems for statistics based on spacings
1997 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The maximum spacing (MSP) method, introduced by Cheng and Amin (1983) and independently by Ranneby (1984), is a general estimation method for continuous univariate distributions. The MSP method, which is closely related to the maximum likelihood (ML) method, can be derived from an approximation based on simple spacings of the Kullback-Leibler information. It is known to give consistent and asymptotically efficient estimates under general conditions and works also in situations where the ML method fails, e.g. for the three parameter Weibull model.

In this thesis it is proved under general conditions that MSP estimates of parameters in the Euclidian metric are strongly consistent. The ideas behind the MSP method are extended and a class of estimation methods is introduced. These methods, called generalized MSP methods, are derived from approxima­tions based on sum-functions of rath order spacings of certain information mea­sures, i.e. the ^-divergences introduced by Csiszår (1963). It is shown under general conditions that generalized MSP methods give consistent estimates. In particular, it is proved that generalized MSP methods give L1 consistent esti­mates in any family of distributions with unimodal densities, without any further conditions on the distributions. Other properties such as distributional robust­ness are also discussed. Several limit theorems for sum-functions of rath order spacings are given, for ra fixed as well as for the case when ra is allowed to in­crease to infinity with the sample size. These results provide a strongly consistent nonparametric estimator of entropy, as well as a characterization of the uniform distribution. Further, it is shown that Cressie's (1976) goodness of fit test is strongly consistent against all continuous alternatives.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, 1997. 30 p.
Keyword
Estimation, spacings, maximum spacing method, consistency, (^-divergence, goodness of fit, unimodal density, entropy estimation, uniform distribution
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-85176 (URN)91-7191-328-9 (ISBN)
Projects
digitalisering@umu
Available from: 2014-01-30 Created: 2014-01-29 Last updated: 2014-01-30Bibliographically approved

Open Access in DiVA

Maximum spacing estimates based on different metrics(884 kB)251 downloads
File information
File name FULLTEXT01.pdfFile size 884 kBChecksum SHA-512
87170e39efd0e67062b24fe49a176b8b46d8207ea55f28a4139af5d7f842d1d2ebe39a9984acc705193189912962efb740cfce555896782592f4222418979bd2
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Ekström, Magnus
By organisation
Mathematical statistics
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar
Total: 251 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 106 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf