Large sample properties of maximum likelihood estimator using moving extremes ranked set sampling

In this paper, we investigate the maximum likelihood estimator (MLE) for the parameter \(\theta\) in the probability density function \(f(x;\theta )\). We specifically focus on the application of moving extremes ranked set sampling (MERSS) and analyze its properties in large samples. We establish the existence and uniqueness of the MLE for two common distributions when utilizing MERSS. Our theoretical analysis demonstrates that the MLE obtained through MERSS is, at the very least, as efficient as the MLE obtained through simple random sampling with an equivalent sample size. To substantiate these theoretical findings, we conduct numerical experiments. Furthermore, we explore the implications of imperfect ranking and provide a practical illustration by applying our approach to a real dataset.