Using Liu estimator for detection of influential observations in linear measurement error models

In this paper, we introduce Liu estimator for the vector of parameters in linear measurement error models and discuss its asymptotic properties. Based on the Liu estimator, diagnostic measures are developed to identify influential observations. Additionally, the analogs of Cook's distance and likelihood distance are proposed to determine influential observations using case deletion approach. A parametric bootstrap procedure is used to obtain empirical distributions of the test statistics. Finally, the performance of the influence measures have been illustrated through simulation study and analyzing a real data set.