Strong limit theorems for sums of logarithms of high order spacings

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.

Keywords

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

Published in

Statistics
1999, volume: 33, number: 2, pages: 153-169

SLU Authors

• Ekström, Magnus

  • Umeå University

UKÄ Subject classification

Probability Theory and Statistics

Publication identifier

• DOI: https://doi.org/10.1080/02331889908802689

Permanent link to this page (URI)

https://res.slu.se/id/publ/100465