Strong limit theorems for sums of logarithms of mth order spacings
1997 (English)Report (Other academic)
Several strong limit theorems axe proved for sums of logarithms of mth order spacings from general distributions. In all given results, the order of 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. 
 Research was supported by The Bank of Sweden Tercentenary Foundation.
Place, publisher, year, edition, pages
Umeå: Umeå universitet , 1997. , 14 p.
, Research report / Department of Mathematical Statistics, Umeå University, ISSN 1401-730X ; 1997:7
Spacings, Strong limit theorems, Entropy estimation, Uniform distribution, Goodness of fit
Probability Theory and Statistics
IdentifiersURN: urn:nbn:se:umu:diva-85173OAI: oai:DiVA.org:umu-85173DiVA: diva2:691966