<abstract xmlns="http://www.w3.org/1999/xhtml">The paper presents a new (to the best of the authors’ knowledge) estimator of probability called the “Eph √ 2 completeness estimator” along with a theoretical derivation of its optimality. The estimator is especially suitable for a small number of sample items, which is the feature of many real problems characterized by data insufficiency. The control parameter of the estimator is not assumed in an a priori, subjective way, but was determined on the basis of an optimization criterion (the least absolute errors).The estimator was compared with the universally used frequency estimator of probability and with Cestnik’s m-estimator with respect to accuracy. The comparison was realized both theoretically and experimentally. The results show the superiority of the Eph √ 2 completeness estimator over the frequency estimator for the probability interval ph ∈ (0.1, 0.9). The frequency estimator is better for ph ∈ [0, 0.1] and ph ∈ [0.9, 1].</abstract>

The paper presents a new (to the best of the authors’ knowledge) estimator of probability called the “Eph √ 2 completeness estimator” along with a theoretical derivation of its optimality. The estimator is especially suitable for a small number of sample items, which is the feature of many real problems characterized by data insufficiency. The control parameter of the estimator is not assumed in an a priori, subjective way, but was determined on the basis of an optimization criterion (the least absolute errors).The estimator was compared with the universally used frequency estimator of probability and with Cestnik’s m-estimator with respect to accuracy. The comparison was realized both theoretically and experimentally. The results show the superiority of the Eph √ 2 completeness estimator over the frequency estimator for the probability interval ph ∈ (0.1, 0.9). The frequency estimator is better for ph ∈ [0, 0.1] and ph ∈ [0.9, 1].

Optimal estimator of hypothesis probability for data mining problems with small samples

Faculty of Computer Science West Pomeranian University of Technology, Żołnierska 49, 71-210 Szczecin, Poland

Institute of Quantitative Methods Maritime University of Szczecin, Wały Chrobrego 1–2, 70-500 Szczecin, Poland

International Journal of Applied Mathematics and Computer Science

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

The paper presents a new (to the best of the authors’ knowledge) estimator of probability called the “Eph √ 2 completeness estimator” along with a theoretical...

Optimal estimator of hypothesis probability for data mining problems with small samples

Published Online: Sep 28, 2012

Page range: 629 - 645

DOI: https://doi.org/10.2478/v10006-012-0048-z

Keywords
single-case problem, probability, probability estimation, frequency interpretation of probability, completeness interpretation of probability, uncertainty theory

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

Optimal estimator of hypothesis probability for data mining problems with small samples

Published Online: Sep 28, 2012

Page range: 629 - 645

DOI: https://doi.org/10.2478/v10006-012-0048-z

Keywordssingle-case problem, probability, probability estimation, frequency interpretation of probability, completeness interpretation of probability, uncertainty theory

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

Keywords
single-case problem, probability, probability estimation, frequency interpretation of probability, completeness interpretation of probability, uncertainty theory