The asymptotic loss of information for grouped data

JOURNAL OF MULTIVARIATE ANALYSIS

卷:67

Article

Felsenstein, K

关键词: asymptotically optimal discretization;    grouped data;    Kullback-Leibler distance;    optimal quantizer;    optimal design;   

DOI  :  10.1006/jmva.1998.1759

来源: Elsevier

【 摘 要 】

We study the loss of information (measured in terms of the Kullback-Leibler distance) caused by observing grouped data (observing only a discretized version of a continuous random variable). We analyze the asymptotical behaviour of the loss of information as the partition becomes finer. In the case of a univariate observation, we compute the optimal rate of convergence and characterize asymptotically optimal partitions (into intervals). In the multivariate case we derive the asymptotically optimal regular sequences of partitions. Furthermore, we compute the asymptotically optimal transformation of the data, when a sequence of partitions is given. Examples demonstrate the efficiency of the suggested discretizing strategy even for few intervals. (C) 1998 Academic Press

【 授权许可】

Free