Abstract
In the paper, the approach of using rough sets to verifying sufficiency of a statistic is presented. The notions of the rough set approximation operators on statistics, consistency between statistics and its properties are introduced. Then, based on these materials, the results on the sufficiency of a statistic are given.
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Benavoli, A., de Campos, C.P.: Statistical tests for joint analysis of performance measures. In: Suzuki, J., Ueno, M. (eds.) AMBN 2015. LNCS (LNAI), vol. 9505, pp. 76–92. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-28379-1_6
Fraser, D.A.S., Naderi, A.: Minimal sufficient statistics emerge from the observed likelihood functions. Int. J. Stat. Sci. 5(Special Issue) (2006)
Lehmann, E.L.: An interpretation of completeness and Basu’s theorem. J. Am. Stat. Assoc. 76(374), 335–340 (1981)
Lehmann, E.L., Romano, J.P.: Testing Statistical Hypotheses, 3rd edn. Springer Science+Business Media Inc, New York (2005)
Ly, A., Marsman, M., Verhagen, J., Grasman, R.P.P.P., Wagenmakers, E.-J.: A tutorial on Fisher information. J. Math. Psychol. 80, 40–55 (2017)
Martin, R.: Exponential Families, Sufficiency & Information. Stat 511. Lecture Notes II (2014)
Mukhopadhyay, N., Banerjee, S.: Fisher information, sufficiency, and ancillary: some clarifications. In: METRON, vol. 71, pp. 33–38 (2013). https://doi.org/10.1007/s40300-013-0005-0
Park, S., Ng, H.K.T., Chan, P.S.: On the Fisher information and design of a flexible progressive censored experiment. Stat. Probab. Lett. 97, 142–149 (2015)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)
Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inf. Sci. 177, 3–27 (2007)
Ramachandran, K.M., Tsokos, C.P.: Mathematical Statistics with Applications. Elsevier Academic Press (2009)
Stein, M.S., Nossek, J.A., Barbé, K.: Fisher information lower bounds with applications in hardware-aware nonlinear signal processing. arXiv Preprint arXiv:1512.03473v2 [cs.IT] 27 May 2018
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The authors would like to thank all the anonymous reviewers for their comments to improve the quality of the paper.
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Tuyen, H.B., Phuong, T.T.T., Huy, D.P. (2018). Rough Set Approach to Sufficient Statistics. In: Nguyen, H., Ha, QT., Li, T., Przybyła-Kasperek, M. (eds) Rough Sets. IJCRS 2018. Lecture Notes in Computer Science(), vol 11103. Springer, Cham. https://doi.org/10.1007/978-3-319-99368-3_38
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DOI: https://doi.org/10.1007/978-3-319-99368-3_38
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