Abstract
The problem of testing an outlier from a multivariate mixture distribution of several populations has many important applications in practice. One particular example is in monitoring worldwide nuclear testing, where we wish to detect whether an observed seismic event is possibly a nuclear explosion (an outlier) by comparing it with the training samples from mining blasts and earthquakes. The combined population of seismic events from mining blasts and earthquakes can be viewed as a mixture distribution. The classical likelihood ratio test appears to not be applicable in our problem, and in spite of the importance of this problem, little progress has been made in the literature. This article proposes a simple modified likelihood ratio test that overcomes the difficulties in the current problem. Bootstrap techniques are used to approximate the distribution of the test statistic. The advantages of the new test are demonstrated via simulation studies. Some new computational findings are also reported.
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