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Strong limit theorems for sums of logarithms of high order spacings

Publication: Contribution to journalJournal articlepeer-review

Abstract

Several strong limit theorems are proved for sums of logarithms of mth order spacings from general distributions. In all given results, the order m 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.
Original languageEnglish
Pages (from-to)153-169
Number of pages17
JournalStatistics
Volume33
Issue number2
DOIs
Publication statusPublished - 1999
Externally publishedYes

Keywords

  • spacings
  • strong limit theorems
  • entropy estimation
  • uniform distribution
  • goodness of fit

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