Abstract

Sample surveys have been recognized as a way to obtain information on a wide range of topics of interests for a population as a whole but also for a certain sub-populations or domains. For domains or areas with small sample sizes, called small areas, “direct” estimators or estimators that only employ data from the domain may display large variance, in these cases, we may use small area methods. This methods "borrow strength" by using "indirect" estimators that employ the values of the variable of interest from related areas increasing the effective sample size and leading to more efficient estimators. In this thesis, we focus on the so called model based small area estimators, which increase the effective sample size with models that link the data throughout all domains. We study their performance under outcome-dependent sampling designs, that is, when the selection of the units to the sample depends on their values of the variable of interest. More precisely, we consider two types of informative sampling designs. A first type, in which the inclusion probabilities are strictly positive for all population units and cut-off sampling, in which a grouping variable related with the variable of interest divides the population in two strata, with one of the strata being deliberately excluded from selection to the sample, that is, where inclusion probabilities are zero. We are especially interested in the estimation of general non-linear parameters, including poverty indicators, in areas or domains of the population with small sample sizes.