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Testing fuzzy linear hypotheses in linear regression models

Author

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  • Bernhard Arnold
  • Oke Gerke

Abstract

In this paper statistical tests with fuzzily formulated hypotheses are discussed, i.e., hypotheses H 0 and H 1 are fuzzy sets. The classical criteria of the errors of type I and type II are generalized, and this approach is applied to the linear hypothesis in the linear regression model. A sufficient condition to control both generalized criteria simultaneously is presented even in case of testing H 0 against the omnibus alternative H 1 : -H 0 . This is completely different from the classical case of testing crisp complementary hypotheses. Copyright Springer-Verlag 2003

Suggested Citation

  • Bernhard Arnold & Oke Gerke, 2003. "Testing fuzzy linear hypotheses in linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 57(1), pages 81-95, February.
    • Handle: RePEc:spr:metrik:v:57:y:2003:i:1:p:81-95
    DOI: 10.1007/s001840200201
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    References listed on IDEAS

    as
    1. Deirdre N. McCloskey & Stephen T. Ziliak, 1996. "The Standard Error of Regressions," Journal of Economic Literature, American Economic Association, vol. 34(1), pages 97-114, March.
    2. Bernhard Arnold, 1996. "An approach to fuzzy hypothesis testing," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 44(1), pages 119-126, December.
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    Cited by:

    1. Hamzeh Torabi & Javad Behboodian & S. Taheri, 2006. "Neyman–Pearson Lemma for Fuzzy Hypotheses Testing with Vague Data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(3), pages 289-304, December.
    2. Coppi, Renato & Gil, Maria A. & Kiers, Henk A.L., 2006. "The fuzzy approach to statistical analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 1-14, November.

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