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 language | English |
|---|---|
| Pages (from-to) | 153-169 |
| Number of pages | 17 |
| Journal | Statistics |
| Volume | 33 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1999 |
| Externally published | Yes |
Keywords
- spacings
- strong limit theorems
- entropy estimation
- uniform distribution
- goodness of fit
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