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

UKÄ Subject classification

Probability Theory and Statistics


Publication Identifiers

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

Permanent link to this page (URI)

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