<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

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

Control and Cybernetics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Estimating and testing relations and trees on the basis of pairwise comparisons"}

The paper presents an ample account on author’s results, concerning the methods of estimating and testing of relations (equivalence, tolerance, preference) and...

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

Published Online: Feb 24, 2024

Page range: 501 - 522

Received: Oct 01, 2022

Accepted: Nov 01, 2022

DOI: https://doi.org/10.2478/candc-2022-0027

Keywords
pairwise comparisons with random errors, estimation and testing of relations and trees, nearest adjoining order idea

© 2022 Leszek Klukowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Feb 24, 2024

Page range: 501 - 522

Received: Oct 01, 2022

Accepted: Nov 01, 2022

DOI: https://doi.org/10.2478/candc-2022-0027

Keywordspairwise comparisons with random errors, estimation and testing of relations and trees, nearest adjoining order idea

© 2022 Leszek Klukowski, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
pairwise comparisons with random errors, estimation and testing of relations and trees, nearest adjoining order idea