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Bootstrapped tests for epistemic fuzzy data

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Epistemic bootstrap is a resampling algorithm that generates bootstrap real-valued samples based on some epistemic fuzzy data input. We apply this method as a universal basis for various statistical tests which can be then directly used for fuzzy random variables. Two classical goodness-of-fit tests are considered as an example to examine the suggested methodology for both synthetic and real data. The proposed approach is also compared with two other goodness-of-fit tests dedicated directly to fuzzy data.
Rocznik
Strony
277--289
Opis fizyczny
Bibliogr. 35 poz., tab., wykr.
Twórcy
  • Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland
  • Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland
Bibliografia
  • [1] Anderson, T.W. (1962). On the distribution of the two-sample Cramer-von Mises criterion, The Annals of Mathematical Statistics 33(3): 1148-1159.
  • [2] Ban, A., Coroianu, L. and Grzegorzewski, P. (2015). Fuzzy Numbers: Approximations, Ranking and Applications, Polish Academy of Sciences, Warsaw.
  • [3] Chernick, M.R., González-Manteiga, W., Crujeiras, R.M. and Barrios, E.B. (2011). Bootstrap methods, in M. Lovric (Ed.), International Encyclopedia of Statistical Science, Springer, Berlin/Heidelberg, pp. 169-174.
  • [4] Couso, I. and Dubois, D. (2014). Statistical reasoning with set-valued information: Ontic vs. epistemic views, International Journal of Approximate Reasoning 55(7): 1502-1518.
  • [5] De Angelis, D. and Young, G.A. (1992). Smoothing the bootstrap, International Statistical Review 60(1): 45-56.
  • [6] Efron, B. (1979). Bootstrap methods: Another look at the jackknife, Annals of Statistics 7(1): 1-26.
  • [7] Faraz, A. and Shapiro, A.F. (2010). An application of fuzzy random variables to control charts, Fuzzy Sets and Systems 161(20): 2684-2694.
  • [8] Gibbons, J.D. and Chakraborti, S. (2010). Nonparametric Statistical Inference, Chapman and Hall/CRC, New York.
  • [9] Gil, M.A., Lubiano, M.A., Montenegro, M. and López, M.T. (2002). Least squares fitting of an affine function and strength of association for interval-valued data, Metrika 56(2): 97-111.
  • [10] Gil, M., Montenegro, M., González-Rodríguez, G., Colubi, A. and Casals, M. (2006). Bootstrap approach to the multi-sample test of means with imprecise data, Computational Statistics and Data Analysis 51(1): 148-162.
  • [11] González-Rodríguez, G., Montenegro, M., Colubi, A. and Gil, M. (2006). Bootstrap techniques and fuzzy random variables: Synergy in hypothesis testing with fuzzy data, Fuzzy Sets and Systems 157(19): 2608-2613.
  • [12] Grzegorzewski, P. (2008). Trapezoidal approximations of fuzzy numbers preserving the expected interval - Algorithms and properties, Fuzzy Sets and Systems 159(11): 1354-1364.
  • [13] Grzegorzewski, P. (2020). Permutation k-sample goodness-of-fit test for fuzzy data, 2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Glasgow, UK, pp. 1-8.
  • [14] Grzegorzewski, P. and Gadomska, O. (2021). Nearest neighbor tests for fuzzy data, 2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Luxembourg, pp. 1-6.
  • [15] Grzegorzewski, P., Hryniewicz, O. and Romaniuk, M. (2019). Flexible bootstrap based on the canonical representation of fuzzy numbers, Proceedings of the 11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019), Prague, Czech Republic, pp. 490-497.
  • [16] Grzegorzewski, P., Hryniewicz, O. and Romaniuk, M. (2020a). Flexible bootstrap for fuzzy data based on the canonical representation, International Journal of Computational Intelligence Systems 13(1): 1650-1662.
  • [17] Grzegorzewski, P., Hryniewicz, O. and Romaniuk, M. (2020b). Flexible resampling for fuzzy data, International Journal of Applied Mathematics and Computer Science 30(2): 281-297, DOI: 10.34768/amcs-2020-0022.
  • [18] Grzegorzewski, P. and Romaniuk, M. (2021). Epistemic bootstrap for fuzzy data, Joint Proceedings of the IFSAEUSFLAT-AGOP 2021 Conferences, Bratislavia, Slovakia, pp. 538-545.
  • [19] Grzegorzewski, P. and Romaniuk, M. (2022a). Bootstrap methods for epistemic fuzzy data, International Journal of Applied Mathematics and Computer Science 32(2): 285-297, DOI: 10.34768/amcs-2022-0021.
  • [20] Grzegorzewski, P. and Romaniuk, M. (2022b). Bootstrapped Kolmogorov-Smirnov test for epistemic fuzzy data, in D. Ciucci et al. (Eds), Information Processing and Management of Uncertainty in Knowledge-Based Systems, Springer International Publishing, Cham, pp. 494-507.
  • [21] Hesamian, G., Akbari, M.G. and Shams, M. (2023). A goodness-of-fit test based on fuzzy random variables, Fuzzy Information and Engineering 15(1): 55-68.
  • [22] Hesamian, G. and Taheri, S. (2013). Linear rank tests for two-sample fuzzy data: A p-value approach, Journal of Uncertain Systems 7(2): 129-137.
  • [23] Kruse, R. (1982). The strong law of large numbers for fuzzy random variables, Information Sciences 28(3): 233-241.
  • [24] Kwakernaak, H. (1978). Fuzzy random variables. Part I: Definitions and theorems, Information Sciences 15(1): 1-15.
  • [25] Lubiano, M.A., Salas, A., Carleos, C., de la Rosa de Sáa, S. and Gil, M.A. (2017). Hypothesis testing-based comparative analysis between rating scales for intrinsically imprecise data, International Journal of Approximate Reasoning 88: 128-147.
  • [26] Lun, A. (2021). metapod: Meta-Analyses on p-Values of Differential Analyses, R package, http://www.bioconductor.org/packages/release/bioc/html/metapod.html.
  • [27] Montenegro, M., Colubi, A., Casals, M. and Gil, M. (2004). Asymptotic and bootstrap techniques for testing the expected value of a fuzzy random variable, Metrika 59: 31-49.
  • [28] Romaniuk, M. and Grzegorzewski, P. (2023). Resampling fuzzy numbers with statistical applications: Fuzzy Resampling package, The R Journal 15(1): 271-283.
  • [29] Romaniuk, M., Grzegorzewski, P. and Parchami, A. (2023). FuzzySimRes: Simulation and Resampling Methods for Epistemic Fuzzy Data, R package, Version 0.2.0, https://CRAN.R-project.org/package=FuzzySimRes.
  • [30] Romaniuk, M. and Hryniewicz, O. (2021). Discrete and smoothed resampling methods for interval-valued fuzzy numbers, IEEE Transactions on Fuzzy Systems 29(3): 599-611.
  • [31] Simes, R.J. (1986). An improved Bonferroni procedure for multiple tests of significance, Biometrika 73(3): 751-754.
  • [32] Smirnov, N. (1933). Estimate of deviation between empirical distribution functions in two independent samples, Bulletin of Moscow University 2: 3-16.
  • [33] Trutschnig, W., González-Rodríguez, G., Colubi, A. and Gil, M.A. (2009). A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread, Information Sciences 179(23): 3964-3972.
  • [34] Vovk, V. and Wang, R. (2020). Combining p-values via averaging, Biometrika 107(4): 791-808.
  • [35] Xiao, Y. (2012). CvM2SL1Test: L1-Version of Cramer-von Mises Two Sample Tests, R package, https://github.com/cran/CvM2SL1Test.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-2bbe9c1e-0960-4dd9-906e-6fda3c9102df
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