Thresholding Events of Extreme in Simultaneous Monitoring of Multiple Risks

John H. J. Einmahl John H. J. Einmahl is Professor, Department of Econometrics & OR and CentER, Tilburg University, 5000 LE Tilburg, The Netherlands . Jun Li is Assistant Professor, Department of Statistics, University of California, Riverside, CA 92521 . Regina Y. Liu is Professor, Department of Statistics & Biostatistics, Rutgers University, Piscataway, NJ 08854 . This research was supported in part by grants from the National Science Foundation, and the Federal Aviation Administration. The discussion on aviation safety in this article reflects the views of the authors, who are solely responsible for the accuracy of the results presented herein, and does not necessarily reflect the official view or policy of the FAA. The data set used in this article has been partially masked to protect confidentiality. The authors thank the editor and referees for their thoughtful comments, which helped improve the article. They also thank Ana Ferreira and Laurens de Haan for providing many helpful suggestions, particularly concerning the bootstrap procedures, and Deyuan Li for performing the “domain of attraction” checks.

Jun Li John H. J. Einmahl is Professor, Department of Econometrics & OR and CentER, Tilburg University, 5000 LE Tilburg, The Netherlands . Jun Li is Assistant Professor, Department of Statistics, University of California, Riverside, CA 92521 . Regina Y. Liu is Professor, Department of Statistics & Biostatistics, Rutgers University, Piscataway, NJ 08854 . This research was supported in part by grants from the National Science Foundation, and the Federal Aviation Administration. The discussion on aviation safety in this article reflects the views of the authors, who are solely responsible for the accuracy of the results presented herein, and does not necessarily reflect the official view or policy of the FAA. The data set used in this article has been partially masked to protect confidentiality. The authors thank the editor and referees for their thoughtful comments, which helped improve the article. They also thank Ana Ferreira and Laurens de Haan for providing many helpful suggestions, particularly concerning the bootstrap procedures, and Deyuan Li for performing the “domain of attraction” checks.

Regina Y. Liu John H. J. Einmahl is Professor, Department of Econometrics & OR and CentER, Tilburg University, 5000 LE Tilburg, The Netherlands . Jun Li is Assistant Professor, Department of Statistics, University of California, Riverside, CA 92521 . Regina Y. Liu is Professor, Department of Statistics & Biostatistics, Rutgers University, Piscataway, NJ 08854 . This research was supported in part by grants from the National Science Foundation, and the Federal Aviation Administration. The discussion on aviation safety in this article reflects the views of the authors, who are solely responsible for the accuracy of the results presented herein, and does not necessarily reflect the official view or policy of the FAA. The data set used in this article has been partially masked to protect confidentiality. The authors thank the editor and referees for their thoughtful comments, which helped improve the article. They also thank Ana Ferreira and Laurens de Haan for providing many helpful suggestions, particularly concerning the bootstrap procedures, and Deyuan Li for performing the “domain of attraction” checks.

Abstract

This article develops a threshold system for monitoring airline performance. This threshold system divides the sample space into regions with increasing levels of risk and allows instant assessments of risk level of any observed airline performance. Of particular concern is the performance with extreme risk. In this article, a multivariate extreme value theory approach is used to establish thresholds for signaling varying levels of extremeness in the context of simultaneous monitoring of multiple risk measures. The threshold system is justified in terms of multivariate extreme quantiles, and its sample estimator is shown to be consistent. This threshold system applies to general extreme risk management. Finally, a simulation and comparison study demonstrates the good performance of the proposed multivariate extreme quantile estimator. Supplemental materials providing technical details are available online.

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Thresholding Events of Extreme in Simultaneous Monitoring of Multiple Risks

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