Estimation of the Second Moment Based on Rounded Data

Abstract

Sample moments are unbiased estimators of theoretical moments (if the latter exist). In practice, however, observations are rounded under registration, which leads to systematic errors. In [1–3] it was shown that random measurement errors can provide the reduction of rounding errors, when the expectation is estimated by the first sample moment. This gives a possibility to manage the rounding error of the result, if one can add some noise to observations before registration. Moreover, this error can be made arbitrarily small. Now we find conditions under which this takes place for the second moment.