Strong limit theorems for sums of logarithms of high order spacings
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
1999, Volume: 33, number: 2, pages: 153-169
UKÄ Subject classification
Probability Theory and Statistics
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