Improved model fitting approaches under ranked set sampling schemes with application to forest data

Abstract

In this paper, we address the problem of fitting probabilistic models based on several sampling designs that originated from the ranked set sampling (RSS) scheme. Although these sampling designs have been proved to be efficient and/or economical alternatives to simple random sampling (SRS) and RSS, the problem of model fitting still should be properly studied for a complete understanding of their advantages. In this study, we investigated the performance of eight RSS-based designs, among them the recently proposed modified neoteric RSS (Taconeli & Cabral, 2019), combined with six estimation methods in model fitting. Through extensive simulations, we could identify the combinations that provided higher efficiency. The simulated results showed that the RSS-based designs outperformed SRS in model fitting, whereas the Anderson-Darling and maximum product of spacings were the most efficient among the estimation methods. In addition, the Anderson-Darling and maximum product of spacings estimation, combined with the neoteric RSS design and its variants, allowed the highest efficiency under both perfectand imperfect ranking. Additional simulations based on real data set from a forest inventory corroborated these findings.