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Abstract:
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There is often additional information that may not be easily incorporated into the individual components of a mixture distribution. For instance, extreme values of a test may definitely diagnose or rule out a disease. That is, there may be thresholds of perfect accuracy that may be incorporated into mixture models. Unlike the regular truncated distribution approach, which would involve more complicated computations and may result in less stable MLE, our direct and computationally simple method allocates extreme observations into specific components in the EM algorithm of the MLE. Such method maximizes a slightly different likelihood function. However, it greatly improves the stability of the MLE procedure, resulting in much more accurate estimations. The method has been applied successfully to estimate TB infection prevalence rates. Extensive numerical simulations are also conducted.
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