IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i3p633-654.html
   My bibliography  Save this article

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

Author

Listed:
  • 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 Krätschmer, Induktive statistik auf basis unscharfer meßkonzepte am beispiel linearer regressionsmodelle, Unpublished Habilitation Monograph, Faculty of Law and Economics of the University of Saarland, Saarbrücken, 2001] to improve the empirical meaningfulness of the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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(05)00049-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Feldstein, Martin, 1995. "The Effect of Marginal Tax Rates on Taxable Income: A Panel Study of the 1986 Tax Reform Act," Journal of Political Economy, University of Chicago Press, vol. 103(3), pages 551-572, June.
    2. Feldstein, Martin, 1995. "The Effect of Marginal Tax Rates on Taxable Income: A Panel Study of the 1986 Tax Reform Act," Journal of Political Economy, University of Chicago Press, vol. 103(3), pages 551-572, June.
    3. Calzolari, Giorgio, 2012. "Econometric notes," MPRA Paper 71440, University Library of Munich, Germany.
    4. Fernandez-Anaya, Guillermo & Alvarez-Ramirez, Jose & Ibarra-Valdez, Carlos, 2007. "On feedback and stable price adjustment mechanisms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 211-226.
    5. Buhong Zheng, 1997. "Statistical Inferences for Poverty Measures with Relative Poverty Rates," LIS Working papers 167, LIS Cross-National Data Center in Luxembourg.
    6. M. Grazia Pittau & Roberto Zelli, 2001. "Income distribution in Italy: A nonparametric analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 175-189, January.
    7. R. M. Balan & Ioana Schiopu-Kratina, 2004. "Asymptotic Results with Generalized Estimating Equations for Longitudinal data II," RePAd Working Paper Series lrsp-TRS398, Département des sciences administratives, UQO.
    8. Norbert Christopeit & Michael Massmann, 2013. "A Note on an Estimation Problem in Models with Adaptive Learning," Tinbergen Institute Discussion Papers 13-151/III, Tinbergen Institute.
    9. Nagel, Rosemarie & Bühren, Christoph & Frank, Björn, 2017. "Inspired and inspiring: Hervé Moulin and the discovery of the beauty contest game," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 191-207.
    10. T. Paul Schultz, 1980. "An Economic Interpretation of the Decline in Fertiliiy in a Rapidly Developing Country: Consequences of Development and Family Planning," NBER Chapters, in: Population and Economic Change in Developing Countries, pages 209-288, National Bureau of Economic Research, Inc.
    11. Yuan-chin Chang, 2011. "Sequential estimation in generalized linear models when covariates are subject to errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(1), pages 93-120, January.
    12. Zhou, Xian & You, Jinhong, 2004. "Wavelet estimation in varying-coefficient partially linear regression models," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 91-104, June.
    13. Yong Tao & Xiangjun Wu & Tao Zhou & Weibo Yan & Yanyuxiang Huang & Han Yu & Benedict Mondal & Victor M. Yakovenko, 2019. "Exponential structure of income inequality: evidence from 67 countries," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(2), pages 345-376, June.
    14. Jin Zhang, 2020. "Consistency of MLE, LSE and M-estimation under mild conditions," Statistical Papers, Springer, vol. 61(1), pages 189-199, February.
    15. Norbert Christopeit & Michael Massmann, 2010. "Consistent Estimation of Structural Parameters in Regression Models with Adaptive Learning," Tinbergen Institute Discussion Papers 10-077/4, Tinbergen Institute.
    16. Arnoud V. den Boer & Bert Zwart, 2014. "Simultaneously Learning and Optimizing Using Controlled Variance Pricing," Management Science, INFORMS, vol. 60(3), pages 770-783, March.
    17. repec:cte:wsrepe:6351 is not listed on IDEAS
    18. Amsler, Christine & Prokhorov, Artem & Schmidt, Peter, 2016. "Endogeneity in stochastic frontier models," Journal of Econometrics, Elsevier, vol. 190(2), pages 280-288.
    19. Sonsino, Doron & Sirota, Julia, 2003. "Strategic pattern recognition--experimental evidence," Games and Economic Behavior, Elsevier, vol. 44(2), pages 390-411, August.
    20. George Boyne, 1987. "Median voters, political systems and public policies: An empirical test," Public Choice, Springer, vol. 53(3), pages 201-219, January.
    21. Ching-Kang Ing & Ching-Zong Wei, 2005. "A maximal moment inequality for long range dependent time series with applications to estimation and model selection," Econometrics 0508009, University Library of Munich, Germany.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:97:y:2006:i:3:p:633-654. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.