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Incomplete Generalized U ‐Statistics for Food Risk Assessment
Author(s) -
Bertail Patrice,
Tressou Jessica
Publication year - 2006
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2005.00401.x
Subject(s) - jackknife resampling , estimator , statistics , delta method , mathematics , statistic , confidence interval , econometrics
Summary This article proposes statistical tools for quantitative evaluation of the risk due to the presence of some particular contaminants in food. We focus on the estimation of the probability of the exposure to exceed the so‐called provisional tolerable weekly intake (PTWI), when both consumption data and contamination data are independently available. A Monte Carlo approximation of the plug‐in estimator, which may be seen as an incomplete generalized U ‐statistic, is investigated. We obtain the asymptotic properties of this estimator and propose several confidence intervals, based on two estimators of the asymptotic variance: (i) a bootstrap type estimator and (ii) an approximate jackknife estimator relying on the Hoeffding decomposition of the original U ‐statistics. As an illustration, we present an evaluation of the exposure to Ochratoxin A in France.