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Strong limit theorems for sums of logarithms of high order spacings
Umeå University, Faculty of Science and Technology, Mathematical statistics.
1999 (English)In: Statistics (Berlin), ISSN 0233-1888, Vol. 33, no 2, 153-169 p.Article in journal (Refereed) Published
Abstract [en]

Several strong limit theorems are proved for sums of logarithms of mth order spacings from general distributions. In all given results, the order mof the spacings is allowed to increase to infinity with the sample size. These results provide a nonparametric strongly consistent estimator of entropy as well as a characterization of the uniform distribution on [0,1]. Furthermore, it is shown that Cressie's (1976) goodness of fit test is strongly consistent against all continuous alternatives.

Place, publisher, year, edition, pages
Gordon and Breach Publishers, 1999. Vol. 33, no 2, 153-169 p.
Keyword [en]
spacings, strong limit theorems, entropy estimation, uniform distribution, goodness of fit
National Category
Probability Theory and Statistics
Research subject
URN: urn:nbn:se:umu:diva-81165DOI: 10.1080/02331889908802689OAI: diva2:653042
Available from: 2013-10-02 Created: 2013-10-02 Last updated: 2014-01-20Bibliographically approved

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Ekström, Magnus
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