İki bağımsız örneklem için dayanıklı yaklaşımların analizi

Comparing two independent groups has been the subject of many classic studies in applied statistics. Although the most common approach for comparing two independent groups is on the basis of just one reference point, it may provide misleading results and cause missing the important differences among subpopulations of the groups. Determination of the differences in tails of the groups, namely quantiles, can also be of particular concern. This thesis aims to compare two independent groups from a different point of view by utilizing quantiles. Therefore, firstly attention is focused on quantile estimation theory and the newly proposed NO quantile estimator is introduced. NO quantile estimator is computationally practical, has desirable asymptotic properties and is more efficient than some quantile estimators that are commonly used. Following this, NO quantile estimator is used in conjunction with a percentile bootstrap to propose a method that compares two independent groups through multiple quantiles simultaneously. By conducting a series of simulation studies and using some real datasets, the performances of NO quantile estimator and the proposed method for comparing two independent groups are investigated. The proposed method could control the actual type I error rates in almost all cases that are investigated. This method is more preferable than the conventional approaches that considers a single measure of location since it makes a more sensitive comparison by using more than one reference points.