Poisson sampling for spectral estimation in periodically correlated processes

Vincent Monsan

Applicationes Mathematicae (1994)

  • Volume: 22, Issue: 2, page 227-266
  • ISSN: 1233-7234

Abstract

top
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.

How to cite

top

Monsan, Vincent. "Poisson sampling for spectral estimation in periodically correlated processes." Applicationes Mathematicae 22.2 (1994): 227-266. <http://eudml.org/doc/219093>.

@article{Monsan1994,
abstract = {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.},
author = {Monsan, Vincent},
journal = {Applicationes Mathematicae},
keywords = {quartic-mean consistency; periodically correlated processes; spectral density functions; Poisson sampling; correlation functions; spectral densities; continuous-time samples; consistency},
language = {eng},
number = {2},
pages = {227-266},
title = {Poisson sampling for spectral estimation in periodically correlated processes},
url = {http://eudml.org/doc/219093},
volume = {22},
year = {1994},
}

TY - JOUR
AU - Monsan, Vincent
TI - Poisson sampling for spectral estimation in periodically correlated processes
JO - Applicationes Mathematicae
PY - 1994
VL - 22
IS - 2
SP - 227
EP - 266
AB - 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.
LA - eng
KW - quartic-mean consistency; periodically correlated processes; spectral density functions; Poisson sampling; correlation functions; spectral densities; continuous-time samples; consistency
UR - http://eudml.org/doc/219093
ER -

References

top
  1. [1] D. Dehay, Spectral analysis of the covariance kernel of the almost periodically correlated processes, Stochastic Process. Appl., submitted. Zbl0793.62050
  2. [2] H. L. Hurd, An investigation of periodically correlated processes, Ph.D. Dissertation, Duke Univ., Durham, N.C., 1969. 
  3. [3] H. L. Hurd, Periodically correlated processes with discontinuous correlation functions, Theory Probab. Appl. 19 (1974), 804-807. Zbl0326.60064
  4. [4] H. L. Hurd, Nonparametric time series analysis for periodically correlated processes, IEEE Trans. Inform. Theory 35 (1989), 350-359. Zbl0672.62096
  5. [5] E. Masry, Poisson sampling and spectral estimation of continuous-time parameter processes, ibid. 24 (1978), 173-183. Zbl0376.62062
  6. [6] E. Masry and M. C. Lui, Discrete-time spectral estimation of continuous parameter -A new consistent estimate, ibid. 22 (1976), 298-312. Zbl0336.62078
  7. [7] F. Messaci, Estimation de la densité spectrale d'un processus en temps continu par échantillonnage poissonnien, Ph.D. Dissertation, Rouen Univ., 1986. 
  8. [8] H. S. Shapiro and R. A. Silverman, Alias-free sampling of random noise, J. Soc. Indust. Appl. Math. 8 (1960), 225-248. Zbl0121.14204

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.