Using Empirical Likelihood to Combine Data : Application to Food Risk Assessment

This paper introduces an original methodology based on empirical likelihood which aims at combiningdifferent contamination and consumptions surveys in order to provide risk managers witha risk measure taking account of all the available information. This risk index is defined as theprobability that exposure to a contaminant exceeds a safe dose. It is expressed as a non linearfunctional of the different consumption and contamination distributions, more precisely as a generalizedU-statistic. This non linearity and the huge size of the data sets make direct computation ofthe problem unfeasible. Using linearization techniques and incomplete versions of the U-statistic,a tractable “approximated” empirical likelihood program is solved yielding asymptotic confidenceintervals for the risk index. An alternative “Euclidean likelihood program” is also considered, replacingthe Kullback-Leibler distance involved in the empirical likelihood by the Euclidean distance.Both methodologies are tested on simulated data and applied to assess the risk due to the presenceof methyl mercury in fish and other seafoods.