Improved likelihood ratio tests in a measurement error model for multivariate replicated data

We present a measurement error model for multivariate replicated data and focus on the improved likelihood ratio tests for parameters of interest. By assuming that the random terms follow the scale mixtures of normal distributions, the model can bring robust inference and can target on both error-prone and error-free covariates. We derive modified versions from the original likelihood ratio statistics to achieve better asymptotic properties with high degree of accuracy. Simulation studies are conducted to display finite sample behavior as compared to the unmodified counterpart. The practical utility is illustrated through a root decomposition data.