Parameter estimation in the presence of auxiliary information

Dissertação para obtenção do Grau de Doutora em Estatística e Gestão de Risco, Especialidade em Estatística

In survey research, there are many situations when the primary variable of interest is sensitive. The sensitivity of some queries can give rise to a refusal to answer or to false answers given intentionally. Survey can be conducted in a variety of settings, in part dictated by the mode of data collection, and these settings can differ in how much privacy they offer the respondent. The estimates obtained from a direct survey on sensitive questions would be subject to high bias. A variety of techniques have been used to improve reporting by increasing the privacy of the respondents. The Randomized Response Technique (RRT), introduced byWarner in 1965, develops a random relation between the individual’s response and the question. This technique provides confidentiality to respondents and still allows the interviewers to estimate the characteristic of interest at an aggregate level. In this thesis we propose some estimators to improve the mean estimation of a sensitive variable based on a RRT by making use of available non-sensitive auxiliary information. In the first part of this thesis we present the ratio and the regression estimators as well as some generalizations in order to study the gain in the estimation over the ordinary RRT mean estimator. In chapters 4 and 5 we study the performance of some exponential type estimators, also based on a RRT. The final part of the thesis illustrates an approach to mean estimation in stratified sampling. This study confirms some previous results for a different sample design. An extensive simulation study and an application to a real dataset are done for all the study estimators to evaluate their performance. In the last chapter we present a general discussion referring to the main results and conclusions as well as showing an application to a real dataset which compares the performance of study estimators.