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International Work-Conference on Artificial Neural Networks

IWANN 2001: Connectionist Models of Neurons, Learning Processes, and Artificial Intelligence pp 316–324Cite as

Optimal Transformations in Multiple Linear Regression Using Functional Networks

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2084))

Abstract

Functional networks are used to determine the optimal transformations to be applied to the response and the predictor variables in linear regression. The main steps required to build the functional network: selection of the initial topology, simplification of the initial functional network, uniqueness of representation, and learning the parameters are discussed, and illustrated with some examples.

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References

  1. Aczál, J.: Lectures on Functional Equations and Their Applications, Vol. 19. Mathematics in Science and Engineering, Academic Press, New York, (1966)

    Google Scholar 

  2. Atkinson, A. C.: Plots, Transformations and Regression. An Introduction to Graphical Methods of Diagnostic Regression Analysis. Clarendon Press, Oxford, (1985)

    Google Scholar 

  3. Breiman, L., Friedman, J. H.: Estimating Optimal Transformations for Multiple Regression and Correlation (with comments). Journal of the American Statistical Association, Vol. 80, No. 391, (1985) 580-619

    Google Scholar 

  4. Carroll, R. J., Ruppert, D.: Transformations and Weigthing in Regression. Chapman and Hall, (1988)

    Google Scholar 

  5. Castillo, E., Cobo, A., Gutiárrez, J. M., Pruneda, E.: An Introduction to Functional Networks with Applications. Kluwer Academic Publishers: New York, (1998)

    Google Scholar 

  6. Castillo, E., Gutiárrez, J. M., Cobo, A., Castillo, C.: A Minimax Method for Learning Functional Networks. Neural Processing Letters, 11, 1, (2000) 39–49

    Article  Google Scholar 

  7. Castillo, E., Gutiárrez, J. M., Hadi, A. S., Lacruz, B.: Some Aplications of Functional Networks in Statistics and Engineering. Technometrics, (in press), (2001)

    Google Scholar 

  8. Castillo, E., Ruiz-Cobo, R.: Functional Equations in Science and Engineering. Marcel Dekker: New York, (1992)

    MATH  Google Scholar 

  9. Castillo, E. and Gutiárrez, J. M.: Nonlinear Time Series Modeling and Prediction Using Functional Networks. Extracting Information Masked by Chaos. Physics Letters A, Vol. 244, (1998) 71–84

    Article  Google Scholar 

  10. Chaterjee, S., Hadi, A. S., Price, B.: Regression Analysis by Example. Third Edition. John Wiley and Sons, Inc., (2000)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, University of Cantabria, Spain

    Enrique Castillo

  2. Department of Statistical Sciences, Cornell University, USA and Department of Mathematics, The American University in Cairo, Egypt

    Ali S. Hadi

  3. Department of Statistical Methods, University of Zaragoza, Spain

    Beatriz Lacruz

Authors
  1. Enrique Castillo
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  2. Ali S. Hadi
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  3. Beatriz Lacruz
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Editor information

Editors and Affiliations

  1. Departamento de Inteligencia Artificial Sanda del Rey, Universidad Nacional de Educación a Distancia, s/n., Madrid, 28040, Spain

    José Mira

  2. Departamento de Arquitectura y Tecnología de Computadores, Universidad de Granada, Campus Fuentenueva, 18071, Granada, Spain

    Alberto Prieto

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© 2001 Springer-Verlag Berlin Heidelberg

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Castillo, E., Hadi, A.S., Lacruz, B. (2001). Optimal Transformations in Multiple Linear Regression Using Functional Networks. In: Mira, J., Prieto, A. (eds) Connectionist Models of Neurons, Learning Processes, and Artificial Intelligence. IWANN 2001. Lecture Notes in Computer Science, vol 2084. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45720-8_36

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  • DOI: https://doi.org/10.1007/3-540-45720-8_36

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42235-8

  • Online ISBN: 978-3-540-45720-6

  • eBook Packages: Springer Book Archive

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