A minimum volume set of a probability density is a region of minimum size among the regions covering a given probability mass of the density. Effective methods for finding the minimum volume sets are very useful for detecting failures or anomalies in commercial and security applications-a problem known as novelty detection. One theoretical approach of estimating the minimum volume set is to use a density level set where a kernel density estimator is plugged into the optimization problem that yields the appropriate level. Such a plug-in estimator is not of practical use because solving the corresponding minimization problem is usually intractable. A modified plug-in estimator was proposed by Hyndman in 1996 to overcome the computation difficulty of the theoretical approach but is not well studied in the literature. In this paper, we provide theoretical support to this estimator by showing its asymptotic consistency. We also show that this estimator is very competitive to other existing novelty detection methods through an extensive empirical study. ©2010 INFORMS.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: Park and Ding's research was partially supported by grants from the National Science Foundation (CMMI-0348150 and CMMI-0529026). Huang's research was partially supported by grants from the National Science Foundation (DMS-0606580 and DMS-0907170), the National Cancer Institute (CA57030), and award number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST). The authors are also grateful for the insightful comments and constructive suggestions made by the associate editor and two reviewers that helped improve the paper.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.