Optimizing Mean Estimators with Calibrated Minimum Covariance Determinant in Median Ranked Set Sampling

Calibration methods enhance estimates by modifying the initial design weights, for which supplementary information is exploited. This paper first proposes a generalized class of minimum-covariance-determinant (MCD)-based calibration estimators and then presents a novel class of MCD-based calibrated estimators under a stratified median-ranked-set-sampling (MRSS) design. Further, we also present a double MRSS version of generalized and novel classes of estimators. To assess and compare the performance of the generalized and novel classes of estimators, both real and artificial datasets are utilized. In the presented practical scenarios and real-world applications, we utilize information from a dataset comprising 800 individuals in Turkey from 2014. These data include body mass index (BMI) as the primary variable of interest and age values as auxiliary variables. The BMI results shows that the proposed estimators $({\overline{y}}_{P{M}_I}=581.1897,{\overline{y}}_{Pa{M}_I}=544.8397)$ have minimum and $({\overline{y}}_{P{M}_{II}}=669.1822,{\overline{y}}_{Pa{M}_{II}}=648.2363)$ have maximum PREs in the case of single and double MRSS for odd sample sizes. Similarly, $({\overline{y}}_{P{M}_I}=860.0099,{\overline{y}}_{Pa{M}_I}=844.7803)$ have minimum and $({\overline{y}}_{P{M}_{II}}=974.5859,{\overline{y}}_{Pa{M}_{II}}=953.7233)$ have maximum PREs in the case of single and double MRSS for even sample sizes. Additionally, we conduct a simulation study using a symmetric dataset.