Local asymptotic coding and the minimum description length

Local asymptotic arguments imply that parameter selection via the minimum description length (MDL) resembles a traditional hypothesis test. A common approximation for MDL estimates the cost of adding a parameter at about (1/2)log n bits for a model fit to n observations. While accurate for parameter...

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Bibliographic Details
Published in:IEEE transactions on information theory 1999-05, Vol.45 (4), p.1289-1293
Main Authors: Foster, D.P., Stine, R.A.
Format: Article
Language:English
Subjects:
Approximation
Asymptotic properties
Codes
Coding
Costs
Data compression
Electrical engineering
Encoding
Estimates
Estimators
Hypotheses
Mathematical analysis
Mathematical models
Parametric statistics
Random variables
Source coding
Standard error
Testing
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Summary:Local asymptotic arguments imply that parameter selection via the minimum description length (MDL) resembles a traditional hypothesis test. A common approximation for MDL estimates the cost of adding a parameter at about (1/2)log n bits for a model fit to n observations. While accurate for parameters which are large on a standardized scale, this approximation overstates the parameter cost near zero. We find that encoding the parameter produces a shorter description length when the corresponding estimator is about two standard errors away from zero, as in a traditional statistical hypothesis test.
ISSN:0018-9448
1557-9654
DOI:10.1109/18.761287