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Multivariate Non-Linear Regression with Applications

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References

  1. M. Arató, A. N. Kolmogorov, and J. G. Sinay. Evaluation of the parameters of a complex stationary Gauss-Markov process. Dokl. Akad. Nauk SSSR, 146:747–750, 1962.

    MATH  Google Scholar 

  2. V. V. Anh, N. N. Leonenko, and L. M. Sakhno. Quasilikelihood-based higher-order spectral estimation of random processes and fields with possible long-range dependence. J. of Appl. Probab., 41A:35–54, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  3. T. W. Anderson. The statistical analysis of time series. Wiley, New York, 1971.

    MATH  Google Scholar 

  4. D. R. Brillinger. An empirical investigation of the chandler wobble and two proposed excitation processes. Bull. Int. Statist. Inst., 45(3):413–434, 1973.

    Google Scholar 

  5. D. R. Brillinger. Time Series; Data Analysis and Theory. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2001. Reprint of the 1981 edition.

    Google Scholar 

  6. E. N. Brown. A note on the asymptotic distribution of the parameter estimates for the harmonic regression model. Biometrika, 77(3):653–656, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  7. K. Choy and M. Taniguchi. Stochastic regression model with dependent disturbances. J. Time Ser. Anal., 22(2):175–196, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Dahlhaus. Efficient location and regression estimation for long range dependent regression models. Ann. Statist., 23(3):1029–1047, 1995.

    MATH  MathSciNet  Google Scholar 

  9. U. Grenander and M. Rosenblatt. Statistical Analysis of Stationary Time Series. Wiley, New York, 1957.

    MATH  Google Scholar 

  10. U. Grenander. On the estimation of regression coefficients in the case of an autocorrelated disturbance. Ann. Math. Statistics, 25:252–272, 1954.

    MATH  MathSciNet  Google Scholar 

  11. R. S. Gross. The excitation of the chandler wobble. Geophys. Res. Lett., 27(15):2329, 2000.

    Article  Google Scholar 

  12. X. Guyon. Random Fields on a Network Modeling, Statistics, and Applications. Springer-Verlag, New York, 1995.

    MATH  Google Scholar 

  13. E. J. Hannan. Multiple Time Series. Springer-Verlag, New York, 1970.

    MATH  Google Scholar 

  14. E. J. Hannan. Non-linear time series regression. Applied Probability Trust, pages 767–780, 1971.

    Google Scholar 

  15. E. J. Hannan. The asymptotic theory of linear time series models. J. Appl. Proab., 10:130–145, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  16. C. C. Heyde. Quasi-Likelihood and Its Application. Springer Series in Statistics. Springer-Verlag, New York, 1997.

    MATH  Google Scholar 

  17. Y. Hosoya. A limit theory for long-range dependence and statistical inference on related models. Ann. Statist., 25(1):105–137, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  18. I. A. Ibragimov and Yu. A. Rozanov. Gaussian Random Processes. Springer-Verlag, New York, 1978. Translated from the Russian by A. B. Aries.

    MATH  Google Scholar 

  19. E. Iglói and Gy. Terdik. Bilinear modelling of Chandler wobble. Theor. of Probab. Appl., 44(2):398–400, 1997.

    Google Scholar 

  20. E. Iglói and Gy. Terdik. Superposition of diffusions with linear generator and its multifractal limit process. ESAIM Probab. Stat., 7:23–88 (electronic), 2003.

    Article  MATH  MathSciNet  Google Scholar 

  21. R. I. Jennrich. Asymptotic properties of non-linear least squares estimators. Ann. Math. Statist., 40:633–643, 1969.

    MATH  MathSciNet  Google Scholar 

  22. C. Klüppelberg and T. Mikosch. The integrated periodogram for stable processes. Ann. Statist., 24(5):1855–1879, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  23. I. Lobato. Consistency of the averaged cross-periodogram in long memory series. J. Time Series Anal., 18(2):137–155, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  24. I. N. Lobato. A semiparametric two-step estimator in a multivariate long memory model. J. Econometrics, 90(1):129–153, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  25. J. R. Magnus and H. Neudecker. Matrix Differential Calculus with Applications in Statistics and Econometrics. Wiley, Chichester, 1999. Revised reprint of the 1988 original.

    MATH  Google Scholar 

  26. P. M. Robinson and F. J. Hidalgo. Time series regression with long-range dependence. Ann. Statist., 25(1):77–104, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  27. P. M. Robinson. Non-linear regression for multiple time-series. J. Appl. Probab., 9:758–768, 1972.

    Article  MATH  Google Scholar 

  28. H. Schuh, T. Nagel, and T. Seitz. Linear drift and periodic variations observed in long time series of polar motion. J. Geodesy, 74:701–710, 2001.

    Article  Google Scholar 

  29. Gy. Terdik. Higher order statistics and multivariate vector Hermite polynomials for nonlinear analysis of multidimensional time series. Teor. Imovīr. Mat. Stat., 66:147–168, 2002.

    MATH  Google Scholar 

  30. J. Wang. Asymptotics of least-squares estimators for constrained nonlinear regression. Ann. Statist., 24(3):1316–1326, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  31. L. Wang. Asymptotics of estimates in constrained nonlinear regression with long-range dependent innovations. Ann. Inst. Statist. Math., 56(2):251–264, 2004.

    MATH  MathSciNet  Google Scholar 

  32. Chien-Fu Wu. Asymptotic theory of nonlinear least squares estimation. Ann. Statist., 9(3):501–513, 1981.

    MATH  MathSciNet  Google Scholar 

  33. Y. Yajima. On estimation of a regression model with long-memory stationary errors. Ann. Statist., 16(2):791–807, 1988.

    MATH  MathSciNet  Google Scholar 

  34. Y. Yajima. Asymptotic properties of the LSE in a regression model with long-memory stationary errors. Ann. Statist., 19(1):158–177, 1991.

    MATH  MathSciNet  Google Scholar 

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Rao, T.S., Terdik, G. (2006). Multivariate Non-Linear Regression with Applications. In: Bertail, P., Soulier, P., Doukhan, P. (eds) Dependence in Probability and Statistics. Lecture Notes in Statistics, vol 187. Springer, New York, NY . https://doi.org/10.1007/0-387-36062-X_19

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