In surveys, one may face the problem of influential units at the estimation stage. A unit is said to be influential if its inclusion or exclusion from the sample has a drastic impact on the estimates. This is a common situation in business surveys as the distribution of economic variables tends to be highly skewed. We study and examine some commonly used estimators and predictors of a population total and propose a robust estimator and predictor based on an adaptive tuning constant. The proposed tuning constant is based on the concept of conditional bias of a unit, which is a measure of influence. We present the results of a simulation study that compares the performance of several estimators and predictors in terms of bias and efficiency.

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Dans certaines enquêtes auprès des entreprises, il n'est pas rare de s'intéresser à estimer le total ou la moyenne d'une variable qui, par sa nature, prend souvent une valeur nulle. En présence d'une grande proportion de valeurs nulles, les estimateurs usuels peuvent s'avérer inefficaces. Dans ce mémoire, nous étudions les propriétés des estimateurs habituels pour des populations exhibant une grande proportion de zéros. Dans un contexte d'une approche fondée sur le modèle, nous présentons des prédicteurs robustes à la présence de valeurs influentes pour ce type de populations. Finalement, nous effectuons des études par simulation afin d'évaluer la performance de divers estimateurs/prédicteurs en termes de biais et d'efficacité. / In business surveys, we are often interested in estimating population means or totals of variables which, by nature, will often take a value of zero. In the presence of a large proportion of zero-valued observations, the customary estimators may be unstable. In this thesis, we study the properties of commonly used estimators for populations exhibiting a large proportion of zero-valued observations. In a model-based framework, we present some robust predictors in the presence of influential units. Finally, we perform simulation studies to evaluate the performance of several estimators in terms of bias and efficiency.