Consistency of orthogonal series density estimators based on grouped observations

In this correspondence we show that nonparametric orthogonal series estimators of probability densities retain the mean integrated square error (MISE) consistency when observations are grouped to the points of a uniform grid (prebinned). This kind of grouping is typical for computer rounding errors...

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Bibliographic Details
Published in:IEEE transactions on information theory 1997-01, Vol.43 (1), p.283-285
Main Author: Rafajlowicz, E.
Format: Article
Language:English
Subjects:
Analog-digital conversion
Bibliographies
Computer errors
Data compression
Data engineering
Fast Fourier transforms
Information technology
Kernel
Probability
Probability density function
Roundoff errors
Sampling methods
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Summary:In this correspondence we show that nonparametric orthogonal series estimators of probability densities retain the mean integrated square error (MISE) consistency when observations are grouped to the points of a uniform grid (prebinned). This kind of grouping is typical for computer rounding errors and may also be useful in data compression, before calculating estimates, e.g., using the FFT. The main result shows that MISE consistency holds for all square-integrable densities under mild conditions on the grid step size.
ISSN:0018-9448
1557-9654
DOI:10.1109/18.567707