Strong Limit Theorems for Sums of Logarithms of High Order Spacings
Strong Limit Theorems for Sums of Logarithms of High Order Spacings
复制标题
高阶间距对数和的强极限定理
DOI：
10.1080/02331889908802689
复制
发表时间：
1999
期刊：
影响因子：
1.9
通讯作者：
M. Ekström
中科院分区：
文献类型：
--
作者：
M. Ekström
本文证明了一般分布的m阶空间的多项式和的几个强极限定理。在所有给定的结果中，允许间距的阶数m随样本大小增加到无穷大。这些结果提供了熵的非参数强相合估计以及[0，1]上均匀分布的特征。此外，还证明了Cressie（1976）的拟合优度检验对所有连续型方案都是强一致的.
Several strong limit theorems are proved for sums of logarithms of mth order spacings from general distributions. In all given results, the order mof 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.