Sheppard's correction for variances and the "quantization noise model"

In this paper, we examine the relevance of Sheppard's correction for variances and (both the original and a valid weak form of) the so-called "quantization noise model" to understanding the effects of integer rounding on continuous random variables. We further consider whether there i...

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Bibliographic Details
Published in:IEEE transactions on instrumentation and measurement 2005-10, Vol.54 (5), p.2117-2119
Main Author: Vardeman, S.B.
Format: Article
Language:English
Subjects:
Analysis of variance
Dithering
Electrical engineering
histogram density
Histograms
independent
Instrumentation
Integers
Joints
Manufacturing industries
Manufacturing systems
Mathematical models
Noise
Quantization
Random variables
Rounding
Statistical distributions
Systems engineering and theory
uncorrelated
uniform distribution
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Summary:In this paper, we examine the relevance of Sheppard's correction for variances and (both the original and a valid weak form of) the so-called "quantization noise model" to understanding the effects of integer rounding on continuous random variables. We further consider whether there is any real relationship between the two. We observe that the strong form of the model is not really relevant to describing rounding effects. We demonstrate using simple cases the substantial limitations of the Sheppard correction, and use simple versions of a weak form of the model to establish that there is no real connection between the correction and the model.
ISSN:0018-9456
1557-9662
DOI:10.1109/TIM.2005.853348