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Bootstrap tests for mean value differences over fuzzy samples


Nikolova, N and Mihaylova, N and Tenekedjiev, K, Bootstrap tests for mean value differences over fuzzy samples, Proceedings of the 16th IFAC Conference on Technology, Culture and International Stability, 24-27 September 2015, Sozopol, Bulgaria, pp. 7-14. ISSN 2405-8963 (2015) [Refereed Conference Paper]

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Copyright 2015 IFAC

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DOI: doi:10.1016/j.ifacol.2015.12.048


This 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.

Item Details

Item Type:Refereed Conference Paper
Keywords:fuzzy samples, percentile Bootstrap procedure, simulation-based algorithm, generalization of drawing-with-replacement procedure, fuzzy mean value
Research Division:Mathematical Sciences
Research Group:Statistics
Research Field:Applied statistics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the information and computing sciences
UTAS Author:Nikolova, N (Professor Nataliya Nikolova)
UTAS Author:Tenekedjiev, K (Professor Kiril Tenekedjiev)
ID Code:106432
Year Published:2015
Deposited By:NC Maritime Engineering and Hydrodynamics
Deposited On:2016-02-10
Last Modified:2016-08-05

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