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Strong consistency of least-squares estimation in linear regression models with vague concepts

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  • Krätschmer, Volker

Abstract

Linear regression models with vague concepts extend the classical single equation linear regression models by admitting observations in form of fuzzy subsets instead of real numbers. They have recently been introduced [cf. Krätschmer, Induktive statistik auf basis unscharfer meßkonzepte am beispiel linearer regressionsmodelle, Unpublished Habilitation Monograph, Faculty of Law and Economics of the University of Saarland, Saarbrücken, 2001] to improve the empirical meaningfulness of the relationship between the involved items by a more sensitive attention to the problems of data measurement, in particular the fundamental problem of adequacy. The parameters of such models are still real numbers, and a method of estimation can be applied which extends directly the ordinary least-squares method. This paper deals with some first asymptotic properties of estimators obtained by the method. Firstly, strong consistency will be shown, and secondly, the convergence rate will be investigated. The later result will be the starting point for a future study which will calculate the limit distributions of the estimators.

Suggested Citation

  • Krätschmer, Volker, 2006. "Strong consistency of least-squares estimation in linear regression models with vague concepts," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 633-654, March.
  • Handle: RePEc:eee:jmvana:v:97:y:2006:i:3:p:633-654
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    1. N/A, 1976. "Chapter III. the World Economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 75(1), pages 33-63, February.
    2. Lai, T. L. & Robbins, Herbert & Wei, C. Z., 1979. "Strong consistency of least squares estimates in multiple regression II," Journal of Multivariate Analysis, Elsevier, vol. 9(3), pages 343-361, September.
    3. N/A, 1976. "Chapter I. The Home Economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 76(1), pages 6-24, May.
    4. N/A, 1976. "Chapter I. The Home Economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 77(1), pages 7-32, August.
    5. N/A, 1976. "Chapter II. The World Economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 76(1), pages 25-44, May.
    6. Toye, J. F. J., 1976. "Economic Theories of Politics and Public Finance," British Journal of Political Science, Cambridge University Press, vol. 6(4), pages 433-447, October.
    7. N/A, 1976. "Chapter II. The World Economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 78(1), pages 21-39, November.
    8. anonymous, 1976. "The economy in 1975," Federal Reserve Bulletin, Board of Governors of the Federal Reserve System (U.S.), issue Feb, pages 71-81.
    9. N/A, 1976. "Chapter II. The World Economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 77(1), pages 33-49, August.
    10. repec:ilo:ilowps:168467 is not listed on IDEAS
    11. N/A, 1976. "Chapter I. The Home Economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 78(1), pages 6-20, November.
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    Cited by:

    1. Lopez-Diaz, Miguel & Ralescu, Dan A., 2006. "Tools for fuzzy random variables: Embeddings and measurabilities," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 109-114, November.
    2. Giordani, Paolo, 2010. "Three-way analysis of imprecise data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 568-582, March.
    3. 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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