Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1996-1997 | 24 | 4 | 357-381
Tytuł artykułu

Statistical estimation of higher-order spectral densities by means of general tapering

Treść / Zawartość
Warianty tytułu
Języki publikacji
Given a realization on a finite interval of a continuous-time stationary process, we construct estimators for higher order spectral densities. Tapering and shift-in-time methods are used to build estimators which are asymptotically unbiased and consistent for all admissible values of the argument. Asymptotic results for the fourth-order densities are given. Detailed attention is paid to the nth order case.
Opis fizyczny
  • UFR des Sciences-Mathématiques, URA CNRS 1378, site Colbert, Université de Rouen, 76821 Mont Saint Aignan Cedex, France
  • [1] M. Baba Harra, Estimation de densités spectrales d'ordre quatre avec lissage quelconque, Publication de l'URA 1378 Analyse et Modèles Stochastiques 2 (1995), 1-38.
  • [2] M. Baba Harra, Estimation de densités spectrales d'ordre élevé, PhD thesis, Université de Rouen, 1996.
  • [3] A. Blanc-Lapierre et R. Fortet, Théorie des Fonctions Aléatoires, Masson, Paris, 1953.
  • [4] P. Bloomfield, Fourier Analysis of Time Series: An Introduction, Wiley, New York, 1976.
  • [5] D. R. Brillinger, An introduction to polyspectra, Ann. Math. Statist. 36 (1965), 1351-1374.
  • [6] D. R. Brillinger, Time Series: Data Analysis and Theory, Holt, Rinehart and Winston, New York, 1975.
  • [7] D. R. Brillinger, The 1983 Wald memorial lectures: Some statistical methods for random process data from seismology and neurophysiology, Ann. Statist. 16 (1988), 1-54.
  • [8] D. R. Brillinger and M. Rosenblatt, Asymptotic theory of estimates of k-th order spectra, in: B. Harris (ed.), Advanced Seminar on Spectral Analysis of Time Series, Wiley, New York, 1967, 153-231.
  • [9] J. W. Cooley and J. W. Tukey, An algorithm for the machine calculation of complex Fourier series, Math. Comp. 19 (1965), 297-301.
  • [10] R. Dahlhaus, Spectral analysis with tapered data, J. Time Ser. Anal. 4 (1983), 163-175.
  • [11] R. Dahlhaus, Nonparametric spectral analysis with missing observations, Sankhyā 3 (1987), 347-367.
  • [12] S. Elgar and V. Chandran, Higher order spectral analysis of Chua's circuit, IEEE Trans. Circuit Systems, 40 (1993), 689-692.
  • [13] U. Grenander and M. Rosenblatt, Statistical Analysis of Stationary Time Series, Wiley, New York, 1957.
  • [14] G. A. Isakova, Estimation spectrale d'ordre élevé pour les processus stationnaires avec lissage gaussien, C. R. l'Acad. Sci. République Sov. Biélorussie 3 (1989), 3-9.
  • [15] R. H. Jones, Spectral analysis with regularly missed observations, Ann. Math. Statist. 33 (1962), 455-461.
  • [16] P. T. Kim, Estimation of product moments of a stationary stochastic process with application to estimation of cumulants and cumulant spectral densities, Canad. J. Statist. 17 (1989), 285-299.
  • [17] L. H. Koopmans, The Spectral Analysis of Time Series, Academic Press, New York, 1974.
  • [18] Le Fe Do, Strong consistency of an estimate of a moment function of fourth order of a stationary random process, Ukrain. Mat. Zh. 49 (1991), 354-358 (in Russian).
  • [19] V. P. Leonov and A. N. Shiryaev, On a method of calculation of semi-invariants, Theor. Probab. Appl. 4 (1959), 319-329.
  • [20] K. S. Lii and M. Rosenblatt, Cumulant spectral estimates: Bias and covariance, in: Limit Theorems in Probability and Statistics (Pécs, 1989), Colloq. Math. Soc. János Bolyai 57, North-Holland, 1990, 365-405.
  • [21] K. S. Lii, M. Rosenblatt and C. W. Atta, Bispectral measurements in turbulence, J. Fluid Mech. 77 (1976), 45-62.
  • [22] A. Preumont, Vibrations aléatoires et analyse spectrale, Presses Polytechniques et Universitaires Romandes, Lausanne, 1990.
  • [23] M. B. Priestley, Spectral Analysis and Time Series, Academic Press, London, 1981.
  • [24] M. Rosenblatt and J. Van Ness, Estimation of the bispectrum, Ann. Math. Statist. 36 (1965), 1120-1135.
  • [25] A. N. Shiryaev, Some problems in the spectral theory of higher-order moments, Theor. Probab. Appl. 5 (1961), 265-284.
  • [26] T. Subba Rao and M. M. Gabr, An Introduction to Bispectral Analysis and Bilinear Time Series Models, Lecture Notes in Statist. 24, Springer, New York, 1984.
  • [27] I. G. Žurbenko [I. G. Zhurbenko], The Spectral Analysis of Time Series, North-Holland, Amsterdam, 1986.
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.