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Gaussian semiparametric estimation for random fields with singular spectrum

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Języki publikacji
EN
Abstrakty
EN
We analyze the asymptotic behaviour of the tapered discrete Fourier transforms for random fields with singular spectrum. The results are used to establish consistency and asymptotic normality for semiparametric estimates of the singularity parameter under broad conditions.
Rocznik
Strony
105--138
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
  • Dipartimento di Matematica, Università di Roma '"Tor Vergata", via della Ricerca Scientifica 1, 00133 Roma, Italy
Bibliografia
  • [1] S. Albeverio, S. A. Molchanov and D. Surgailis, Stratified structure of the Universe and Burgers' equation: Probabilistic approach, Probab. Theory Related Fields 100 (1994), pp. 457-484.
  • [2] V. V. Anh, J. M. Angulo and M. D. Ruiz-Medina, Possible long-range dependence in fractional random fields, J. Statist. Plann. Inference 80 (1999), pp. 95-110.
  • [3] V. V. Anh and N. N. Leonenko, Non-Gaussian scenario for the heat equation with singular initial conditions, Stochastic Process. Appl. 84 (1999), pp. 91-114.
  • [4] V. V. Anh and N. N. Leonenko, Scaling laws for fractional diffusion-wave equations with singular data, Statist. Probab. Lett., to appear.
  • [5] T. Funaki, D. Surgailis and W. A. Woyczyński, Gibbs-Cox random fields and Burgers turbulence, Ann. Appl. Probab. 5 (1995), pp. 461-492.
  • [6] X. Guyon, Random Fields on a Network: Modelling, Statistics and Applications, Springer, Berlin 1995.
  • [7] E. J. Hannan, Multiple Time Series, Wiley, New York 1970.
  • [8] C. C. Heyde and R. Gay, Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence, Stochastic Process. Appl. 45 (1993), pp. 169-182.
  • [9] A. V. Ivanov and N. N. Leonenko, Statistical Analysis of Random Fields, Kluwer Academic Publishers, Dordrecht 1989.
  • [10] G. W. Kolb and M. S. Turner, The Early Universe, Addison and Wesley, Redwood City, CA, 1990.
  • [11] H. R. Künsch, Statistical analysis of self-similar processes, in: Proceedings of the 1st World Congress of the Bernoulli Society, VNU Science Press, 1987, pp. 67-74.
  • [12] N. N. Leonenko, Random Fields with Singular Spectrum, Kluwer Academic Publishers, Dordrecht 1999.
  • [13] N. N. Leonenko and W. A. Woyczynski, Exact parabolic asymptotics for singular n-D Burgers' random fields: Gaussian approximation, Stochastic Process. Appl. 76 (1998), pp. 141-165.
  • [14] N. N. Leonenko and W. A. Woyczynski, Parameter identification for singular random fields arising in Burgers' turbulence, J. Statist. Plann. Inference 80 (1999), pp. 1-14.
  • [15] N. N. Leonenko and W. A. Woyczynski, Parameter identification for stochastic Burgers' flows via parabolic rescaling, Probab. Math. Statist. 21, No. 1 (2001), pp. 1-55.
  • [16] C. Ludena and M. Lavielle, The Whittle estimator for strongly dependent stationary Gaussian fields, Scand. J. Statist. 26 (1999) pp. 433-450.
  • [17] S. A:Molchanov, D. Surgailis and W. A. Woyczynski, The large scale structure of the Universe and quasi-Voronoi tessellation of shock fronts in forced Burgers turbulence in Rd, Ann. Appl. Probab. 7 (1997), pp. 200-228.
  • [18] J. Peebles, Principles of Physical Cosmology, Princeton University Press, Princeton 1990.
  • [19] D, B. Percival and A. T. Walden, Spectral Analysis with Physical Applications, Cambridge University Press, Cambridge 1993.
  • [20] P. M. Robinson, Log-periodogram regression of time series with long-range dependence, Ann. Statist. 23 (1995), pp. 1048-1072.
  • [21] P. M. Robinson, Gaussian semiparametric estimation of long-range dependence, Ann. Statist. 23 (1995), pp. 1630-1661.
  • [22] S. F. Shandarin and Y. B. Zeldovich, The large-scale structure of the Universe: Turbulence, intermittency, structures in a self-gravitating medium, Rev. Modern Phys., Vol. 1, No. 2 (1989), pp. 185-220.
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  • [24] C. Velasco, Non-Gaussian log-periodogram regression, Econom. Theory 16, No. 1 (2000), pp. 44-79.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a6670217-f839-4828-8a7d-da68a42348a9
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