Statistical Analysis for Rounded Data

Abstract

Unless the model is discrete, rounding of data is unavoidable in practical measurement. However, the errors caused by rounding of data are almost ignored by all classical statistical theories. Inconsistencies of sample mean and sample variance of rounded data are shown in this paper. T-test and chi-square test show that the true value of mean and variance are rejected in this paper. Although some pioneers have noticed this problem, few suitable approaches were proposed to deal with this error. In this paper, by some concrete examples when measurements are rounded to some extent, we propose to use MLE or approximated MLE (AMLE) to estimate the parameters and discuss the properties of them and tests based on the new estimators. In particular, as an example, we shall discuss the limiting properties of the new estimator of parameters in an AR(p) model and MA(q) model when the observations are rounded. This is a joint work with Zhidong Bai, Baoxue Zhang and Guorong Hu