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Research article - Peer-reviewed, 1999

Strong limit theorems for sums of logarithms of high order spacings

Ekstrom, M


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.


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

Published in

1999, Volume: 33, number: 2, pages: 153-169

    UKÄ Subject classification

    Probability Theory and Statistics

    Publication Identifiers


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