The Asymptotic Loss of Information for Grouped Data
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.
Year of publication: |
1998
|
---|---|
Authors: | Felsenstein, Klaus ; Pötzelberger, Klaus |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 67.1998, 1, p. 99-127
|
Publisher: |
Elsevier |
Keywords: | Asymptotically optimal discretization grouped data Kullback-Leibler distance optimal quantizer optimal design |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
Bayesian analysis of co-integrated time series
Felsenstein, Klaus, (1989)
-
Estimating the dimension of factors of diffusion processes
Pötzelberger, Klaus, (2003)
-
CLUSTERING AND QUANTIZATION BY MSP-PARTITIONS
Pötzelberger, Klaus, (2001)
- More ...