Symmetric and Asymmetric Rounding

If rounded data are used in estimating moments and regression
coefficients, the estimates are typically more or less biased. The
purpose of the paper is to study the bias inducing effect of
rounding, which is also seen when population moments instead of
their estimates are considered. Under appropriate conditions this
effect can be approximately specified by versions of Sheppard's
correction formula. We discuss the conditions under which these
approximations are valid. We also investigate the efficiency loss
that comes along with rounding. The rounding error, which
corresponds to the measurement error of a measurement error model,
has a marginal distribution which can be approximated by the
uniform distribution. We generalize the concept of simple rounding
to that of asymmetric rounding and study its effect on the mean and
variance of a distribution under similar circumstances as with
simple rounding.