A Note on Rounding Error in The Variables: Understanding Its Influence on Statistical Estimators

Abstract

AbstractWhen estimating the variance, higher moments, and regression coefficients using rounded data, bias is commonly introduced into these estimates. Sheppard’s correction can be used to approximately adjust for this bias under certain conditions. This study investegated the conditions that allow for the valid application of Sheppard’s corrections. A significant observation from the research was that the rounding error-often displaying a uniform distribution-was not independent of the original, unrounded variable. The study provided a thorough investigation of instances where variables, distributed uniformly, undergo rounding. This investigation yielded crucial insights into the statistical behavior and potential ramifications of such variables within statistical analyses. An integral part of this study was the computation and discussion of the density function of the rounding error. Deriving this density function facilitated a nuanced analysis of the differences between the moments of rounded data and the original, unrounded data. Sheppard’s regularities, under which Sheppard’s correction is applied, were discussed. The letter also carefully considered the effects of rounding error on regression estimates. In this context, Sheppard’s correction was implemented to the biased regression parameters to evaluate its efficacy in providing more accurate estimations. Further, our research provides new insights into how rounding can affect statistical outcomes, depending on the underlying distribution of the data. We have discovered that the impact is minimal under uniform distribution assumptions but becomes significantly pronounced under non-uniform distributions. This highlights the importance of considering the distributional characteristics of data when applying rounding corrections to ensure the reliability of statistical inferences.