Symmetric and asymmetric rounding: a review and some new results

Abstract

Using rounded data to estimate moments and regression coefficients typically biases the estimates. We explore the bias-inducing effects of rounding, thereby reviewing widely dispersed and often half forgotten results in the literature. Under appropriate conditions, these effects can be approximately rectified by versions of Sheppard’s correction formula. We discuss the conditions under which these approximations are valid and also investigate the efficiency loss caused by 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, but is not independent of the true value. In order to take account of rounding preferences (heaping), we generalize the concept of simple rounding to that of asymmetric rounding and consider its effect on the mean and variance of a distribution.