Quantifying Rounding-Induced Error for Non-Negative Discrete Random Variables

• Activity Number: 444 - Recent Advances in Statistical Methodology for Big Data
• Type: Contributed
• Date/Time: Thursday, August 12, 2021 : 4:00 PM to 5:50 PM
• Sponsor: IMS
• Author(s): Roberto Rivera and Axel Cortes Cubero* and Roberto Reyes and Wolfgang Rolke
• Companies: University of Puerto Rico at Mayaguez and University of Puerto Rico at Mayaguez and University of Puerto Rico at Mayaguez
• Keywords: Rounding error; Fourier transform; Sheppard's correction; binning; maximum likelihood estimator; big data

Abstract

Rounding to the nearest integer data corresponding to continuous random variables is known to introduce a quantifiable error, when inferring the parameters of the distribution. Rounding may be applied to functions of discrete random variables as well. In this presentation, we study the scenario when a rounded to nearest integer average is used to estimate counts. Specifically, our interest is in drawing inference on a parameter from the PMF of count $Y$, when we must use $U = n[Y/n]$ as a proxy for $Y$. The probability generating function of $U$, $E(U)$, and $Var(U)$ are developed for any nonnegative discrete random variable. Some example applications will show how the rounding can have significant impact on inference.