Testing statistical hypotheses with vague data

Przemysław Grzegorzewski

Abstract

A definition of fuzzy test for testing statistical hypotheses with vague data is proposed. Then the general method for the construction of fuzzy tests for hypotheses concerning an unknown parameter against one-sided or two-sided alternative hypotheses is shown. This fuzzy test, contrary to the classical approach, leads not to the binary decision: to reject or to accept given null hypothesis, but to a fuzzy decision showing a grade of acceptability of the null and the alternative hypothesis, respectively. However, it is a natural generalization of the traditional test, i.e. if the data are precise, not vague, we get a classical statistical test with the binary decision. A measure of fuzziness of the considered fuzzy test is suggested and the robustness of that test is also discussed.
Author Przemysław Grzegorzewski (FMIS / DSPFM)
Przemysław Grzegorzewski,,
- Department of Stochastic Processes and Financial Mathematics
Journal seriesFuzzy Sets and Systems, ISSN 0165-0114
Issue year2000
Vol112
No3
Pages501-510
Keywords in EnglishFuzzy data, Fuzzy test, Hypothesis testing
ASJC Classification1702 Artificial Intelligence; 2609 Logic
DOIDOI:10.1016/S0165-0114(98)00061-X
URL http://www.sciencedirect.com/science/article/pii/S016501149800061X
Score (nominal)40
Publication indicators WoS Citations = 53; Scopus Citations = 72; Scopus SNIP (Source Normalised Impact per Paper): 2014 = 2.278 - 2014=2.278; WoS Impact Factor: 2007 = 1.618 (5) - 2006=1.181 (2)
Citation count*126 (2015-08-19)
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