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The Asymptotic Loss of Information for Grouped Data

Felsenstein, Klaus and Pötzelberger, Klaus (1995) The Asymptotic Loss of Information for Grouped Data. Forschungsberichte / Institut für Statistik, 46. Department of Statistics and Mathematics, WU Vienna University of Economics and Business, Vienna.

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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)

Item Type: Paper
Keywords: Asymptotically optimal discretization / grouped data / Kullack-Leibler distance / optimal quantizer / optimal design
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Depositing User: Repository Administrator
Date Deposited: 11 Jul 2006 12:41
Last Modified: 17 Jul 2015 01:36
URI: http://epub.wu.ac.at/id/eprint/1432

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