Pairwise Comparison Based Ranking Vector Approach to Estimation Performance Ranking

Given multiple statistical estimators, how to rank their performance is a worthwhile problem. We propose an approach to estimation performance ranking based on pairwise comparison. Because ranking is about two or more estimators and is relative, pairwise comparison (e.g., Pitman's measure of closeness) suits the needs. However, pairwise comparison cannot guarantee transitivity, which is needed for ranking. To get around this problem, we propose a ranking vector (RV) approach based on pairwise comparison. Here, an RV is obtained by using pairwise comparison results without using pairwise ranks directly. An RV provides ordinal information determining the rank and also supplementary cardinal information exhibiting how much one estimator is better than another. Ordinal information is more important and thus is guaranteed by using an order-preserving mapping in obtaining an RV. Our RV approach based on pairwise comparison is also applied to multiple-attribute decision problems. The approach is easily applicable and it does not need data normalization.