Detection of Outliers and Influential Observations in Linear Ridge Measurement Error Models with Stochastic Linear Restrictions

The aim of this paper is to propose some diagnostic methods in linear ridge measurement error models with stochastic linear restrictions using the corrected likelihood. Based on the bias-corrected estimation of model parameters, diagnostic measures are developed to identify outlying and influential observations. In addition, we derive the corrected score test statistic for outliers detection based on mean shift outlier models. The analogues of Cookʹs distance and likelihood distance are proposed to determine influential observations based on case deletion model. A parametric bootstrap procedure is used to obtain empirical distributions of the test statistics and a simulation study has been given to show the performance of the score test statistic. Finally, the proposed diagnostic procedures are illustrated on a numerical example to show the theoretical results.