A Computable Plug-In Estimator of Minimum Volume Sets for Novelty Detection

Chiwoo Park (), Jianhua Z. Huang () and Yu Ding ()
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Chiwoo Park: Department of Industrial and Systems Engineering, Texas A&M University, College Station, Texas 77843
Jianhua Z. Huang: Department of Statistics, Texas A&M University, College Station, Texas 77843
Yu Ding: Department of Industrial and Systems Engineering, Texas A&M University, College Station, Texas 77843

Operations Research, 2010, vol. 58, issue 5, 1469-1480

Abstract: 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.

Keywords: density level sets; minimum volume sets; novelty detection; generalized statistical control chart; plug-in estimator; asymptotic consistency (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (4)

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