Strong Limit Theorems for Sums of Logarithms of rath Order Spacings
نویسنده
چکیده
Several strong limit theorems axe proved for sums of logarithms of mth order spacings from general distributions. In all given results, the order of the spac ings is allowed to increase to infinity with the sample size. These results provide a nonparametric strongly consistent estimator of entropy as well a s a charac terization 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. 1
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