Symmetric and asymmetric rounding

If rounded data are used in estimating moments and regression coffiecients, 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 intstead 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.