Evaluation of maximum likelihood procedures in ranked set sampling under imperfect ranking

Abstract

Ranked set sampling (RSS) is a cost-efficient alternative to simple random sampling (SRS) when ranking small sets of population units is much simpler than effectively measuring them. Maximum likelihood estimation (MLE) in RSS is usually based on the restrictive assumption of perfect ranking, assuming that the sample units lead to order statistics. However, this procedure is not flexible and often produces highly biased estimators when ranking errors are present. To remedy these constraints, in this work we suggest and evaluate alternative MLE procedures for RSS: (i) MLE based on the perfect ranking assumption; (ii) MLE based on the SRS assumptions; (iii) a weighted estimator derived from (i) and (ii); (iv) the choice of (i) or (ii) by testing the null hypothesis of perfect ranking. We carried out extensive simulations to investigate the efficiency of each strategy, which allowed us to conclude that although (i) performed the best under perfect ranking, (ii-iv) are preferable under imperfect ranking. We have also evaluated a parametric bootstrap algorithm to obtain confidence intervals in RSS based on the suggested estimators. Two applications using data from age determination of fishes and anthropometric measures of athletes illustrate and corroborate our findings.