Analysis of rounded data in measurement error regression

The measurement error model (MEM) is an important model in statistics because in a regression problem, the measurement error of the explanatory variable will seriously affect the statistical inferences if measurement errors are ignored. In this paper, we revisit the MEM when both the response and explanatory variables are further involved with rounding errors. Additionally, the use of a normal mixture distribution to increase the robustness of model misspecification for the distribution of the explanatory variables in measurement error regression is in line with recent developments. This paper proposes a new method for estimating the model parameters. It can be proved that the estimates obtained by the new method possess the properties of consistency and asymptotic normality.