The Asymptotic Loss of Information for Grouped Data
AbstractWe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 67 (1998)
Issue (Month): 1 (October)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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