Estimation of ordinal population with multi-observer ranked set samples using ties information

In many surveys, we often deal with situations where measuring the study variable is expensive; however, there are easy-to-measure characteristics which can be used as ranking information to obtain more representative samples from the population. Ranked set sampling is successfully employed in these cases as an alternative to commonly used simple random sampling. When the data is ordinal categorical, it is common to apply the ordinal logistic regression approach to ranked set sampling data for the estimation of parameters. This technique first depends on the information of training data. Besides, one is not capable of using the ranking information in the estimation process. In this paper, we propose a ranked set sampling scheme in which ranking information from multiple sources can be combined and incorporated efficiently into both data collection and estimation. The ranked set sampling data is used for non-parametric and maximum likelihood estimation of ordinal categorical population. Through extensive simulation studies, the performance of estimators is evaluated. The methods are finally applied to analyze bone disorder data and obesity data.