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The sign test for interval-valued data. (English) Zbl 1373.62220

Ferraro, Maria Brigida (ed.) et al., Soft methods for data science. Selected papers based on the presentations at the 8th international conference on soft methods in probability and statistics, SMPS 2016, Rome, Italy, September 12–14, 2016. Cham: Springer (ISBN 978-3-319-42971-7/pbk; 978-3-319-42972-4/ebook). Advances in Intelligent Systems and Computing 456, 269-276 (2017).
Summary: Two versions of the generalized sign test for interval-valued data are proposed. Each version correspond to a different view on the interval outcomes of the experiment – either the epistemic or the ontic one. As it is shown, each view yield different approaches to data analysis and statistical inference.
For the entire collection see [Zbl 1355.62005].

MSC:

62G86 Nonparametric inference and fuzziness
62G10 Nonparametric hypothesis testing
Full Text: DOI

References:

[1] Couso I, Dubois D (2014) Statistical reasoning with set-valued information: ontic vs. epistemic views. Int J approximate Reasoning 55:1502–1518 · Zbl 1407.62032 · doi:10.1016/j.ijar.2013.07.002
[2] Filzmoser P, Viertl R (2004) Testing hypotheses with fuzzy data. The fuzzy p-value. Metrika 59:21–29 · Zbl 1052.62009 · doi:10.1007/s001840300269
[3] Grzegorzewski P (1998) Statistical inference about the median from vague data. Control Cybern 27:447–464 · Zbl 0945.62038
[4] Grzegorzewski P (2001) Fuzzy tests–defuzzification and randomization. Fuzzy Sets Syst 118:437–446 · Zbl 0996.62013 · doi:10.1016/S0165-0114(98)00462-X
[5] Grzegorzewski P (2004) Distribution-free tests for vague data. In: Lopez-Diaz M et al (eds) Soft methodology and random information systems. Springer, Heidelberg, pp 495–502 · Zbl 1064.62052 · doi:10.1007/978-3-540-44465-7_61
[6] Grzegorzewski P, Ramos-Guajardo AB (2015) Similarity based one-sided tests for the expected value and interval data. In: Proceedings of EUSFLAT 2015. Atlantis Press, pp 960–966 · doi:10.2991/ifsa-eusflat-15.2015.135
[7] Kreinovich V, Servin C (2015) How to test hypotheses when exact values are replaced by intervals to protect privacy: case of t-tests. Departamental Technical Reports (CS). Paper 892. University of Texas at El Paso
[8] Montenegro M, Casals MR, Colubi A, Gil MA (2008) Testing two-sided hypothesis about the mean of an interval-valued random set. In: Dubois D et al. (eds) Soft Methods for handling variability and imprecision. Springer, pp 133–139 · doi:10.1007/978-3-540-85027-4_17
[9] Nguyen HT, Kreinovich V, Wu B, Xiang G (2012) Computing statistics under interval and fuzzy uncertainty. Springer · Zbl 1238.68009 · doi:10.1007/978-3-642-24905-1
[10] Ramos-Guajardo AB (2014) Similarity test for the expectation of a random interval and a fixed interval. In: Grzegorzewski P et al. (eds) Strengthening links between data analysis and soft computing. Springer, pp 175–182
[11] Ramos-Guajardo AB, Colubi A, González-Rodríguez G (2014) Inclusion degree tests for the Aumann expectation of a random interval. Inf Sci 288:412–422 · Zbl 1357.62088 · doi:10.1016/j.ins.2014.08.013
[12] Sinova B, Casals MR, Colubi A, Gil AM (2010) The median of a random interval. In: Borgelt C et al. (eds) Combining soft computing and statistical methods in data analysis. Springer, pp 575–583 · doi:10.1007/978-3-642-14746-3_71
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