Empirical likelihood estimation in multivariate mixture models with repeated measurements

Abstract

Multivariate mixtures are encountered in situations where the data are repeated or clustered measurements in the presence of heterogeneity among the observations with unknown proportions. In such situations, the main interest may be not only in estimating the component parameters, but also in obtaining reliable estimates of the mixing proportions. In this paper, we propose an empirical likelihood approach combined with a novel dimension reduction procedure for estimating parameters of a two-component multivariate mixture model. The performance of the new method is compared to fully parametric as well as almost nonparametric methods used in the literature.

Keywords:

• Empirical likelihood
• estimating equation
• repeated measurements
• multivariate mixture model

Acknowledgements

The authors would like to thank the editor, the AE, and the referee for their insightful comments and suggestions. The authors would like to thank Dr Jing Qin for valuable discussions and many helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research is partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grants (RGPIN-2018-05846, RGPIN-2018-05981), the National Natural Science Foundation of China (Grant Numbers 11771144, 11501354 and 11501208), and the Chinese 111 Project (B14019).

Notes on contributors

Yuejiao Fu

Yuejiao Fu is an Associate Professor of Statistics in the Department of Mathematics and Statistics at York University, Canada. She received her PhD in Statistics in 2004 from the University of Waterloo. Her research interests include mixture models, empirical likelihood, and statistical genetics.

Yukun Liu

Yukun Liu is a Professor in the School of Statistics, Faculty of Economic and Management, East China Normal University, China. He received his PhD in Statistics in 2009 from Nankai University, China. His research interests include nonparametric and semiparametric statistics based on empirical likelihood and their applications in case-control data, capture-recapture data, selection biased data, and finite mixture models.

Hsiao-Hsuan Wang

Hsiao-Hsuan Wang received her PhD in Statistics in 2010 from York University, Canada. She is now a director in Model Quantification, Enterprise Risk Management, CIBC, Canada.

Xiaogang Wang

Xiaogang Wang is a Professor in Statistics in the Department of Mathematics and Statistics of York University. He is also holding an adjunct position as a senior research fellow at the Institute of Data Science of Tsinghua University in Beijing. He received his PhD in Statistics from the University of British Columbia in 2001. His current research is on statistical analysis of complex data in health and life sciences.