Overcoming ranking errors in regression: Fisher information via minimum ranked unequal-size set sampling design

We establish the first complete theoretical framework for minimum ranked set sampling design with unequal set sizes (MinRSSDU) by deriving the exact Fisher information matrix for simple linear regression parameters with replicated observations. Numerical results demonstrate that MinRSSDU substantially outperforms simple random sampling design (SRSD), with asymptotic relative efficiencies reaching up to 2.0 for slope estimation under normal and logistic distributions. Through extensive Monte Carlo simulations, we show that the maximum likelihood estimators under MinRSSDU consistently achieve lower mean squared errors than their SRS counterparts across some ranking error levels. Our results establish MinRSSDU as a theoretically rigorous and computationally efficient alternative to both SRSD and conventional ranked set sampling design (RSSD) for regression analysis, offering a compelling solution to the ranking error problem that has long constrained the application of RSSD.