Abstract
Robustness is an important problem in statistics. However, robustness of statistical procedures for vague data cannot be limited to insensitivity to departures from assumptions on the underlying distributions. Since the shapes of membership functions applied for modelling vague data are generally strongly subjective one may ask about the influence of these shapes on further decisions.Thus the robustness of the statistical procedures to data representation is also of interest.
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References
Box, G.E.P., Anderson, S.L.: Permutation theory in the derivation of robust criteria and study of departures from assumptions. J. Roy Statist. Soc. Ser. B 17, 1–34 (1955)
Denœux, T., Masson, M.H., Hébert, P.A.: Nonparametric rank-based statistics and significance tests for fuzzy data. Fuzzy Sets Syst. 153, 1–28 (2005)
Grzegorzewski, P.: The robustness against dependence of nonparametric tests for the two-sample location problem. Appl. Math. 22, 469–476 (1995)
Grzegorzewski, P.: Robustness against dependence of some nonparametric tests. Discuss. Math. Algebra Stochastic. Methods 15, 203–212 (1995)
Grzegorzewski, P.: Statistical inference about the median from vague data. Control Cybernet 27, 447–464 (1998)
Grzegorzewski, P.: Testing statistical hypotheses with vague data. Fuzzy Sets Syst. 112, 501–510 (2000)
Grzegorzewski, P.: Distribution-free tests for vague data. In: Lawry, J., Miranda, E., Bugarin, A., Li, S., Gil, M.A., Grzegorzewski, P., Hryniewicz, O. (eds.) Soft Methods for Integrated Uncertainty Modelling. Advances in Soft Computing, vol. 37, pp. 495–502. Springer, Berlin (2004)
Hampel, F.R.: A general qualitative definition of robustness. Ann. Math. Statist. 42, 1887–1896 (1971)
Huber, P.J.: Robust Statistics. Wiley Series in Probability and Statistics. Wiley, New York (1981)
Kwakernaak, H.: Fuzzy random variables, Part I: Definitions and theorems. Inform. Sci. 15, 1–15 (1978); Fuzzy random variables, Part II: Algorithms and examples for the discrete case. Inform. Sci. 17, 253–278 (1979)
Puri, M.L., Ralescu, D.A.: Fuzzy random variables. J. Math. Anal. Appl. 114, 409–422 (1986)
Zieliński, R.: Robustness: a quantitative approach. Bull. Acad. Polon. Sci. Ser. Math. Astr. Phi. 24, 1281–1286 (1977)
Zieliński, R.: Robustness of the one-sided Mann-Whitney-Wilcoxon test to dependency between samples. Statist. Probab. Lett. 10, 291–295 (1990)
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Grzegorzewski, P. (2008). Statistics with Vague Data and the Robustness to Data Representation. In: Dubois, D., Lubiano, M.A., Prade, H., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O. (eds) Soft Methods for Handling Variability and Imprecision. Advances in Soft Computing, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85027-4_13
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DOI: https://doi.org/10.1007/978-3-540-85027-4_13
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