ModEls for LEft-censored and Zero-inflated data, with application to Environment.

• Auteur / Autrice : Magdalena Pereda vivo
• Direction : Christian Paroissin
• Type : Projet de thèse
• Discipline(s) : Mathématiques
• Date : Inscription en doctorat le 26/07/2022
• Etablissement(s) : Pau
• Ecole(s) doctorale(s) : Sciences Exactes et leurs Applications
• Partenaire(s) de recherche : Laboratoire : Laboratoire de Mathématiques et de leurs Applications de Pau

Mots clés

Mots clés libres

Statistique

Censure

Limite de détection

Statistic

Censure

Limit of detection

Résumé

Les méthodes analytiques ne permettent pas de mesurer avec précisions des « petites » quantités ; c'est ce qu'on appelle la limite de détection ou de quantification d'une méthode. En terme statistique, cela se traduit par des mesures censurées à gauche. Par ailleurs, dans certaines situations, on peut être confronté à une absence de la substance considérée (absence totale d'un polluant, par exemple) et donc avoir des « vrais » zéros. L'étude de modèles statistiques non-paramétriques pour des données soumises à un mécanisme de censure à gauche et avec excès de zéro reste une domaine peu étudié. L'objectif de ce projet vise à investiguer ce domaine et de développer des outils de surveillance (cartes de contrôle) de mesures (par exemple, des paramètres physico-chimiques). Les modèles et méthodes développés dans ce projet seront appliqués à des données issues de la littérature (données géologiques) ainsi qu'à des données ouvertes de plus grande taille (qualité de l'air).

In many areas (like toxicology, ecotoxicology, chemistry, geosciences and more generally in environmental sciences, as few examples), studies are based on data obtained by some analytical methods. However, these analytical methods cannot measure with certainty quantities that are "too small". This is called "Limit Of Detection" (LOD) (if a quantity can be measured if it is greater than LOD) or "Limit Of Quanti cation" (LOQ) (if a quantity can be detected if it is greater than LOQ) [?]. The presence of data smaller than a given limit (LOD or LOQ) is called, using statistical terms, by data subjected to left censoring. For these data, we only have partial information (since it is not measured exactly). Several strategies have been proposed in the literature (not in the area of statistics) and are sometimes still used. It can be grouped into two categories: the forgetfulness strategy and substitution strategies [?, ?]. The rst strategy consists in ignoring the data which are smaller than the limit (LOD/LOQ) and this leads to get biased estimations. For instance, if we are looking for an average concentration, this will be over-estimated by using such a strategy since we have removed the smaller values (because they are not observed). The second strategy consists in replacing the non-measured values (because smaller than the limit) by a value between 0 and LOD (or LOQ) and the classical choices are the following ones: 0, LOD/2, LOD/ √ 2 et LOD. According to this choice, it will lead either still to over-estimation (if all non-measured values are replaced by LOD) or to under-estimation (if all non-measured values are replaced by 0). In other cases (LOD/2 and LOD/ √ 2), we cannot say what it will give. In addition, in some situations, there could be also the absence of the substance under consideration (a contaminant, for instance) and this will lead to "true" zeros. In statistical terms, we talk about data with zero excess. The combination of data subjected to left censoring (LOD and/or LOQ) and of zero excess make more di cult the statistical treatment.