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Bootstrap tests for mean value differences over fuzzy samples
conference contribution
posted on 2023-05-23, 10:49 authored by Nataliya NikolovaNataliya Nikolova, Mihaylova, N, Kiril TenekedjievKiril TenekedjievThis paper aims to statistically test the null hypothesis H∞ for equality of the mean values of 1D continuous parameter in two different populations, each represented by a fuzzy sample of i.i.d. observations. A degree of membership to the corresponding population is assigned to any of the observations in the fuzzy sample. A Bootstrap algorithm is developed for simulation-based approximation for the CDF of the difference between the sample means, provided that H∞ is true. The needed pvalue of the statistical test is derived using the constructed conditional distribution of the test statistic. The main idea of the proposed Bootstrap test is that, if H∞ is true, then each sample can be shifted so that to have mean value equal to the fuzzy mean value of the united fuzzy sample. The two shifted fuzzy samples are summarized into conditional sample distributions of the 1D continuous parameter used for generation of synthetic couples of fuzzy samples in different pseudo-realities. The proposed algorithm has eight modifications, which differ by the method to generate the synthetic fuzzy sample, by the type of the conditional sample distributions derived from the shifted fuzzy samples, and by the type of the statistical test performed (one-tail or two-tail test). Numerical example are included to demonstrate the proposed algorithm.
History
Publication title
Proceedings of the 16th IFAC Conference on Technology, Culture and International StabilityVolume
48Editors
M Hadjiski, P Groumpos, P Kopacek, A Topalov, K BoshnakovPagination
7-14ISSN
2405-8963Department/School
Australian Maritime CollegePublisher
ElsevierPlace of publication
NetherlandsEvent title
16th IFAC Conference on Technology, Culture and International StabilityEvent Venue
Sozopol, BulgariaDate of Event (Start Date)
2015-09-24Date of Event (End Date)
2015-09-27Rights statement
Copyright 2015 IFACRepository Status
- Restricted