Empirical likelihood for outlier detection in regression models

ABSTRACT

Outlier detection and treatment are important steps in exploratory data analysis. A case deletion method in the empirical likelihood framework is suggested here for outlier detection in regression models. The theoretical properties of empirical likelihood hypothesis testing for outlier detection are investigated and asymptotic results are obtained and compared to the empirical likelihood displacement measure. The behavior of our test statistics in finite samples is studied by means of an extensive simulation experiment and some real data sets. A bootstrap version of the test is also proposed, which proves very useful in the case of data far from normality.

KEYWORDS:

• Statistical hypothesis testing
• leave-one-out statistics
• likelihood ratio test

AMS SUBJECT CLASSIFICATION:

• 62J20
• 62G10

Acknowledgments

The authors thank two anonymous referees and an associate editor for their comments and suggestions that helped to improve the article considerably.

Funding

This research was supported by grant C26A1145RM of the University of Rome La Sapienza, and PRIN national research grant 2010J3LZEN funded by Ministero dell’Istruzione dell’Universita e della Ricerca.

Notes

¹ Integrals were evaluated numerically using the quadrature routines of Matlab.

Additional information

Funding

This research was supported by grant C26A1145RM of the University of Rome La Sapienza, and PRIN national research grant 2010J3LZEN funded by Ministero dell’Istruzione dell’Universita e della Ricerca.