Mean shift and influence measures in linear measurement error models with stochastic linear restrictions

ABSTRACT

We present influence diagnostics for linear measurement error models with stochastic linear restrictions using the corrected likelihood of Nakamura in 1990. The case deletion and mean shift outlier models are developed to identify outlying and influential observations. We derive a corrected score test statistic for outlier detection based on mean shift outlier models. The analogs of Cook's distance and likelihood distance are proposed to determine influential observations based on case deletion models. A parametric bootstrap procedure is used to obtain empirical distributions of the test statistics and a simulation study has been used to evaluate the performance of the proposed estimators based on the mean squares error criterion and the score test statistic. Finally, a numerical example is given to illustrate the theoretical results.

KEYWORDS:

• Case deletion
• Corrected score method
• Influential observations
• Linear measurement error models
• Outlier detection
• Score test

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J07
• 62J20

Acknowledgments

The authors would like to thank the editor and anonymous referees for several helpful comments and suggestions that resulted in a significant improvement in the presentation of this article.