The Asymptotic Loss of Information for Grouped Data

Klaus Felsenstein, Klaus Pötzelberger

Publication: Working/Discussion PaperWU Working Paper

Abstract

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 analyse 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. Forthermore, 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. (author's abstract)
Original languageEnglish
Place of PublicationVienna
PublisherDepartment of Statistics and Mathematics, WU Vienna University of Economics and Business
Publication statusPublished - 1995

Publication series

NameForschungsberichte / Institut für Statistik
No.46

WU Working Paper Series

  • Forschungsberichte / Institut für Statistik

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