Robust estimation of mean and covariance for longitudinal data with dropouts

Abstract

In this paper, we study estimation of linear models in the framework of longitudinal data with dropouts. Under the assumptions that random errors follow an elliptical distribution and all the subjects share the same within-subject covariance matrix which does not depend on covariates, we develop a robust method for simultaneous estimation of mean and covariance. The proposed method is robust against outliers, and does not require to model the covariance and missing data process. Theoretical properties of the proposed estimator are established and simulation studies show its good performance. In the end, the proposed method is applied to a real data analysis for illustration.

Keywords:

• Cholesky decomposition
• longitudinal data
• mean–covariance
• missing data
• robustness

Acknowledgements

The authors are grateful to two referees for their constructive suggestions that largely improve the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was partially supported by the National Nature and Science Foundation of China [11371100, 11271080], the Scientific Research Foundation for the Returned Overseas Chinese Scholars and Shanghai Leading Academic Discipline Project, Project number: B118.

Supplemental data and research materials

Supplemental data for this article can be accessed at 10.1080/02664763.2014.999033.