Before revision: This paper presents the nonparametric inference problem about the probability density function of a latent variable in the measurement error model with repeated measurements.
After revision: Kotlarski's identity has been widely used in applied economic research. However, how to conduct inference based on this popular identification approach has been an open question for two decades. This paper addresses this open problem by constructing a novel confidence band for the density function of a latent variable in the measurement error model with repeated measurements.