Adjustment of model misspecification in estimation of population total under ranked set sampling through balancing

In the model-based approach, researchers assume that the underlying structure, which generates the population of interest, is correctly specified. However, when the working model differs from the underlying true population model, the estimation process becomes quite unreliable due to misspecification bias. Selecting a sample by applying the balancing conditions on some functions of the covariates can reduce such bias. This study aims at suggesting an estimator of population total by applying the balancing conditions on the basis functions of the auxiliary character(s) for the situations where the working model is different from the underlying true model under a ranked set sampling without replacement scheme. Special cases of the misspecified basis function model, i.e. homogeneous, linear, and proportional, are considered and balancing conditions are introduced in each case. Both simulation and bootstrapped studies show that the total estimators under proposed sampling mechanism keep up the superiority over simple random sampling in terms of efficiency and maintaining robustness against model failure.