Extreme Value Theory and Incomplete U-statistics toward Quantitative Evaluation of Food Risk Exposure Related to Some Contaminants

• Activity Number: 325
• Type: Contributed
• Date/Time: Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
• Sponsor: Section on Risk Analysis
• Author(s): Jessica Tressou*+ and Patrice Bertail
• Companies: INR Corela and CREST Paris X Nanterre
• Keywords: food risk assessment ; extreme value theory ; Pareto index ; incomplete U-statistics ; left censorship

Abstract

This paper proposes some statistical methods for evaluating food risk exposure related to some contaminants. We focus on the estimation of the probability of the exposure to exceed the so-called provisional tolerable intake (PTI) when both consumption data and contamination data are independently available. For many contaminants, PTI belongs to the exposure tail distribution, which suggests the use of extreme value theory to evaluate the risk. Our approach consists in modeling the exposure tail by a Pareto-type distribution characterized by a Pareto index which may be seen as a measure of risk. Using propositions by Hall and Feuverger (1999) and Beirlant et al. (1999), we correct the bias of the Hill estimator to precisely estimate the risk index. We compare the results with empirical plug-in methods.This last method simply consists in using a Monte Carlo version of the empirical distribution of the exposure, which may be seen as an incomplete generalized U-statistics (process). This approach is clearly relevant for very risky contaminants. To finish, we present some evaluations and discuss the problem of left censorship appearing in contamination data.