Estimation of a Normal Process Variance from Measurements with Large Round-Off Errors

摘要

Measurements are sometimes affected by excessively large round-off errors. Small rounding-off may safely be ignored for purposes of statistical inference however large rounding-off may have an effect. The importance of the round-off is determined by the ratio between the standard deviation σ and the instrument's scale step h, δ = σ/h.In this paper we estimate σ when δ is small (δ<0.5) using a variant of the Method of Moments (MoM). The MoM estimators are compared with the Maximum Likelihood Estimators (MLE), using simulation. We find that the MoM can improve the estimation in terms of MSE and bias, especially under circumstances where the MLE method is not accurate or cannot provide a solution.