Often in food safety and bio-surveillance it is desirable to estimate the probability that a contaminant or a function thereof exceeds an unsafe high threshold. The probability or chance in question is very small. To estimate such a probability, we need information about large values. In many cases, the data do not contain information about exceedingly large contamination levels, which ostensibly renders the problem insolvable. A solution is suggested whereby more information about small tail probabilities are obtained by combining the real data with computer-generated data repeatedly. This method provides short yet reliable interval estimates based on moderately large samples. An illustration is provided in terms of lead exposure data. Copyright © 2016 John Wiley & Sons, Ltd.
Keywords: NHANES; coverage; density ratio model; food safety; out of sample fusion; semiparametric.
Copyright © 2016 John Wiley & Sons, Ltd.