Poisson sampling for spectral estimation in periodically correlated processes

• Autorzy: Vincent Monsan
• Języki publikacji: EN

Abstrakty

EN

We study estimation problems for periodically correlated, non gaussian processes. We estimate the correlation functions and the spectral densities from continuous-time samples. From a random time sample, we construct three types of estimators for the spectral densities and we prove their consistency.

Słowa kluczowe

EN

quartic-mean consistency; periodically correlated processes; spectral density functions; Poisson sampling

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1993-1995
• Tom: 22
• Numer: 2
• Strony: 227-266

Daty

wydano

1994

otrzymano

1993-01-21

Twórcy

autor

Vincent Monsan

• Laboratoire d'Analyse et Modèles Stochastiques, URA CNRS 1378, Université de Rouen, F-76821 Mont Saint Aignan Cedex, France

Bibliografia

• [1] D. Dehay, Spectral analysis of the covariance kernel of the almost periodically correlated processes, Stochastic Process. Appl., submitted.
• [2] H. L. Hurd, An investigation of periodically correlated processes, Ph.D. Dissertation, Duke Univ., Durham, N.C., 1969.
• [3] H. L. Hurd, Periodically correlated processes with discontinuous correlation functions, Theory Probab. Appl. 19 (1974), 804-807.
• [4] H. L. Hurd, Nonparametric time series analysis for periodically correlated processes, IEEE Trans. Inform. Theory 35 (1989), 350-359.
• [5] E. Masry, Poisson sampling and spectral estimation of continuous-time parameter processes, ibid. 24 (1978), 173-183.
• [6] E. Masry and M. C. Lui, Discrete-time spectral estimation of continuous parameter -A new consistent estimate, ibid. 22 (1976), 298-312.
• [7] F. Messaci, Estimation de la densité spectrale d'un processus en temps continu par échantillonnage poissonnien, Ph.D. Dissertation, Rouen Univ., 1986.
• [8] H. S. Shapiro and R. A. Silverman, Alias-free sampling of random noise, J. Soc. Indust. Appl. Math. 8 (1960), 225-248.