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Covariance approximation of nonlinear regression

  • Statistical Radiophysics
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Abstract

A nonlinear regression model on the basis of the covariance approximation of a multidimensional probability distribution is constructed. The model is represented by an expansion in the basis functions in the form of partial derivatives of the logarithm of the joint factor probability distribution. The weight coefficients of the expansion are the covariances of the resulting and explanatory variables. On particular examples, the efficiency of the Bayesian approximation of the proposed regression model in which the factor distribution is described by a finite mixture of ellipsoidally symmetric densities is demonstrated.

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References

  1. D. W. Scott and R. S. Stephan, “Multi-Dimensional Density Estimation,” Handb. Stat. 24, 229 (2005).

    Google Scholar 

  2. J. Racine, Kvantil’, No. 4, 7 (2008).

    Google Scholar 

  3. E. A. Nadaraya, Teor. Veroyat. Prim. 19 (1), 147 (1964).

    Google Scholar 

  4. G. S. Watson, Sankhya. Indian J. Stat. A26, 359 (1964).

    Google Scholar 

  5. E. A. Nadaraya, Nonparametric Estimation of Probability Density and Regression Curve (Tbilis. Univ., Tbilisi, 1983) [in Russian].

    MATH  Google Scholar 

  6. V. G. Alekseev, Avtom. Telemekh., No. 7, 81 (1988).

    Google Scholar 

  7. W. S. Cleveland, J. Am. Stat. Assoc. 74 (368), 829 (1979).

    Article  MathSciNet  Google Scholar 

  8. D. W. Scott, Multivariate Density Estimation: Theory, Practice and Visualization (Wiley, New York, 1992).

    Book  MATH  Google Scholar 

  9. S. Heiler, A Course in Time Series Analysis, Ed. by D. Pena, G. C. Tiao, and R. S. N. Y. Tsay (Wiley, New York, 2001).

  10. K. V. Voronzov, Lectures on Algorithms for Restoration of Regression (2009). http://www.MachineLearning.ru/wiki/images/a/aa/Voron-ML-Regression.pdf.

    Google Scholar 

  11. S. A. Anatol’ev, Kvantil’, No. 7, 37 (2009).

    Google Scholar 

  12. J. T. Tou and R. C. Gonzalez, Pattern Recognition Principles (Addison-Wesley, Reading, Mass., 1974; Mir, Moscow, 1978).

    MATH  Google Scholar 

  13. S. Haykin, Neural Networks: A Comprehensive Foundation (Prentice-Hall, Upper Saddle River, NJ, 1999; ID “Vil’yams”, Moscow, 2006).

    MATH  Google Scholar 

  14. S. M. A. Bhuiyan, N. O. Atton-Okine, K. E. Barner, et al., Adv. Adaptive Data Analys 1 (2), 309 (2009).

    Article  Google Scholar 

  15. L. Devroye and L. Gyorfii, Nonparametric Density Estimation: The L1 View (Wiley & Sons, New York, 1985; Mir, Moscow, 1988).

    Google Scholar 

  16. L. Breiman, W. Meisel, and E. Purcell, Technometrics 19 (2), 135 (1977).

    Article  Google Scholar 

  17. D. J. Marchette, Wiley Interdisciplinary Reviews: Comput. Stat. 1 (1), 106 (2009).

    Article  Google Scholar 

  18. C. E. Priebe and D. J. Marchette, Pattern Recogn. 26, 771 (1993).

    Article  Google Scholar 

  19. L. V. Labunets, J. Commun. Technol. Electron. 45, 1093 (2000).

    Google Scholar 

  20. L. V. Labunets, N. L. Lebedeva, and M. Yu. Chizhov, J. Commun. Technol. Electron. 57, 577 (2012).

    Article  Google Scholar 

  21. S. A. Aivazyan, V. M. Bukhshtaber, I. S. Enyukov, and L. D. Meshalkin, Applied Statistics: Classification and Reduction in Dimension. Reference Book (Finansy i Statistika, Moscow, 1989) [in Russian].

    MATH  Google Scholar 

  22. M. H. De Groot, Optimal Statistical Decisions (WileyInterscience, 2004; Mir, Moscow, 1974).

    Google Scholar 

  23. K. Fukunaga, Introduction to Statistical Pattern Recognition (Academic, New York, 1972; Nauka, Moscow, 1979).

    MATH  Google Scholar 

  24. M. E. Tipping and C. M. Bishop, Neural Comput. 11, 443 (1999).

    Article  Google Scholar 

  25. A. N. Gorban, B. Kegl, D. C. Wunsch, and A. Y. Zinovyev, Lecture Notes in Computational Science and Engineering (Springer Verlag, Berlin, 2008).

    MATH  Google Scholar 

  26. G. Box and G. Jenkins, Time Series Analysis. Forecasting and Control (Freeman, San Francisco, 1970), Part. 2.

    MATH  Google Scholar 

  27. L. V. Labunets, D. S. Lukin, and A. A. Chervyakov, J. Commun. Technol. Electron. 57, 1265 (2012).

    Article  Google Scholar 

  28. L. V. Labunets, E. L. Labunets, and N. L. Lebedeva, Audit i Finans. Analiz, No. 3, 450 (2014).

    Google Scholar 

  29. R. J. Hyndman, Time Series Data Library. http://datamarket.com/data/list/?q=provider:tsdl).

  30. L. V. Labunets, N. L. Labunets, and M. Yu. Chizhov, J. Commun. Technol. Electron. 56, 1440 (2011).

    Article  Google Scholar 

  31. L. V. Labunets, N. L. Lebedeva, and M. Yu. Chizhov, Vestn. Ros. Nov. Univ., No. 4, 66 (2013).

    Google Scholar 

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 105005, Russia

    L. V. Labunets

  2. Russian New University, ul. Radio 22, Moscow, 105005, Russia

    L. V. Labunets

  3. JSB ROSEVROBANK (JSC), ul. Vavilova 24, Moscow, 119991, Russia

    E. L. Labunets

  4. VTB Bank, ul. Plyushchikha 37, Moscow, 119121, Russia

    N. L. Lebedeva

Authors
  1. L. V. Labunets
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  2. E. L. Labunets
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  3. N. L. Lebedeva
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Correspondence to L. V. Labunets.

Additional information

Original Russian Text © L.V. Labunets, E.L. Labunets, N.L. Lebedeva, 2016, published in Radiotekhnika i Elektronika, 2016, Vol. 61, No. 7, pp. 652–670.

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Labunets, L.V., Labunets, E.L. & Lebedeva, N.L. Covariance approximation of nonlinear regression. J. Commun. Technol. Electron. 61, 789–806 (2016). https://doi.org/10.1134/S106422691607007X

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  • DOI: https://doi.org/10.1134/S106422691607007X

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