Estimation methods for data from nonprobability samples

The main goal of the present dissertation is to evaluate the asymptotic behaviour of estimators for data from nonprobability samples. In this context some target population units do not have positive inclusion probabilities, which means that estimation is affected by biases associated with under-coverage or self-selection errors. For this purpose, we aim at developing a model for the mechanism which caused self-selection in order to estimate the inclusion probabilities for each unit. In this way, pseudo estimators which mimic classical ones can be constructed. More specifically, pseudo Horvitz-Thompson and Hájek estimators are proposed, where propensity score plays the role of inclusion probability. We show that weighting by the inverse of nonparametric estimate of the propensity score leads to an efficient estimate of the population mean. Resampling techniques are used to study the variance asymptotic behaviour and to address the issue of its estimation. A simulation study is carried out in order to assess the validity of the proposed methodology.