Proposals of estimators for the population mean in the presence of nonresponse in simple random sampling

There is an approach in which information about various variables in the estimators used for the estimation of unknown population parameters is fully obtained and there is no missing information. Despite this approach in theory, when the situations that can be encountered in daily life are considered, the information about the variables for the application part may not always be fully obtained. This situation is defined as the non-response case in sampling theory and causes a decrease in the efficiency of the estimators. Therefore, the existence of unobtainable information should be considered for the estimators to be proposed. Hansen and Hurwitz (1946) introduced a new method to cope with the problem of non-response and developed a sub-sampling method for the units that did not respond. Within the scope of the thesis, exponential-type estimators are examined for the population mean estimation in the presence of non-response. The exponential type estimators in the literature are discussed separately for two different non-response cases as Case 1 and Case 2. The aim of the study is to propose an exponential type estimator for the population mean in the case of non-response. According to this aim of the study, after reviewing the method and the estimators in the literature, we propose three different estimators for the population mean estimation in the case of non-response. The proposed estimators are examined in detail for two different non-response cases and efficiency comparisons are made with various estimators in the literature, firstly theoretically and then practically through numerical examples. In addition, in the simulation study, the main estimators in the literature and three different proposed estimators are considered together. It is seen that among all estimators, the most efficient estimator with a relative efficiency value of 5187.87 in Case 1 is the estimator from the proposed family I estimators and in case 2, estimator from the proposed family III estimators is the most efficient estimator with a relative efficiency value of 3700.370.