Estimating and testing relations and trees on the basis of pairwise comparisons

Abstract

Abstract The paper presents an ample account on author’s results, concerning the methods of estimating and testing of relations (equivalence, tolerance, preference) and trees on the basis of multiple pairwise comparisons with random errors, which are presented in a new book, Klukowski (2021c). The book contains also main results presented earlier in Klukowski (2011). The new content pertains mainly to: the preference relation with incomparable elements, trees and tests for verification of estimates of the relations. The estimators and tests have good statistical properties; estimators - consistency with good convergence, tests - known distributions of test statistics (exact, limiting or approximate). Some properties of estimates (precision and convergence) have been determined using the simulation approach. The results here reported gain in significance in view of the renewed interest in practical application of pairwise comparisons in various application domains, which give rise to various concrete data analysis problems.