A1425
Title: Empirical likelihood for unbalanced ranked set sampling
Authors: Seonghun Cho - Inha University (Korea, South) [presenting]
Soohyun Ahn - Ajou University (Korea, South)
Johan Lim - Seoul National University (Korea, South)
Abstract: Unbalanced ranked set sampling (URSS) commonly arises in practice, but incorporating it into the empirical likelihood (EL) framework requires careful handling of unequal stratum sizes. Two EL formulations for inference on the population mean under URSS are investigated. The first approach, termed deterministic balancing, combines the stratum-specific probability constraints into a single weighted normalization constraint. A theoretically justified choice of weights that is aligned with the conventional RSS mean estimator is proposed and the asymptotic distribution of the resulting empirical likelihood ratio statistic is established. The second approach, termed probabilistic balancing, retains the stratum-wise probability constraints and leads to a standard chi-square limiting distribution. The asymptotic properties of both methods are derived and their finite-sample performance is compared through simulation studies. The results show that, although both approaches provide satisfactory control of size, deterministic balancing often yields higher power across a wide range of unbalanced designs. Finally, the proposed methods are applied to test the symmetry of dental size measurements in patients with normal occlusion.
