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 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.