Statistical inference based on ranked set sampling

In a scientific research, the data collection method is substantial for statistical and methodological analysis. Ranked Set Sampling (RSS) is an advanced and effective method for collecting data and making inferences about the population. The main impact of RSS is to use the ranking information of the units in the sampling mechanism. When the ranking is done properly, the inference based on RSS generally gives better results compared with simple random sampling (SRS) for both parametric and non-parametric cases. Because of the uncertain nature of the ranking process without actual measurement, inaccuracy among judgment ranks is unavoidable when using the RSS procedure in a real life application. In this thesis, we propose a new approach for modeling uncertainty in the ranking process and combining the information coming from multiple rankers. A new sampling procedure, Fuzzy-weighted Ranked Set Sampling (FRSS), is introduced for dealing with uncertainty in the ranking mechanism of RSS with fuzzy sets perspective. New methods are introduced to combine the information coming from multiple rankers in FRSS procedure. An estimator for the population mean is defined using the measurements of the sampled units and their membership degrees obtained using the new sampling procedure. We use real data sets from biometric researches and comparative simulation studies to show that our new method results in a considerable improvement on the estimation of the population mean over the counterparts in the literature.