Consistency of Estimators of Cyclic Functional Parameters for Some Nonstationary Processes

Dominique Dehay

Publications mathématiques et informatique de Rennes (1993)

  • Issue: 2, page 1-19

How to cite

top

Dehay, Dominique. "Consistency of Estimators of Cyclic Functional Parameters for Some Nonstationary Processes." Publications mathématiques et informatique de Rennes (1993): 1-19. <http://eudml.org/doc/274440>.

@article{Dehay1993,
author = {Dehay, Dominique},
journal = {Publications mathématiques et informatique de Rennes},
keywords = {spectral density; periodogram; signal theory; cyclic covariance functions; zero mean second order stochastic processes; Fourier series decomposition; almost periodically correlated processes; strongly harmonizable processes; variance; consistency; stochastic spectral measure; mixing condition},
language = {eng},
number = {2},
pages = {1-19},
publisher = {Département de Mathématiques et Informatique, Université de Rennes},
title = {Consistency of Estimators of Cyclic Functional Parameters for Some Nonstationary Processes},
url = {http://eudml.org/doc/274440},
year = {1993},
}

TY - JOUR
AU - Dehay, Dominique
TI - Consistency of Estimators of Cyclic Functional Parameters for Some Nonstationary Processes
JO - Publications mathématiques et informatique de Rennes
PY - 1993
PB - Département de Mathématiques et Informatique, Université de Rennes
IS - 2
SP - 1
EP - 19
LA - eng
KW - spectral density; periodogram; signal theory; cyclic covariance functions; zero mean second order stochastic processes; Fourier series decomposition; almost periodically correlated processes; strongly harmonizable processes; variance; consistency; stochastic spectral measure; mixing condition
UR - http://eudml.org/doc/274440
ER -

References

top
  1. [1] R. C. Bradley and M. Peligrad (1986), Invariance principle under a two part mixing assumption. Stochastic Process. Appl.22, 271-289 Zbl0609.60048MR860937
  2. [2] R. A. Boyles and W. A. Gardner (1983), Cycloergodic properties of discrete-parameter nonstationary stochastic processes, IEEE Transactions on Information Theory IT-29 (1), 105-114. Zbl0513.60045MR711279
  3. [3] C. Corduneanu (1961), Almost periodic functions, Wiley (New York). Zbl0175.09101MR481915
  4. [4] D. Dehay (1991), On the product of two harmonizable processes, Stochastic Process. Appl.39, 347-358 Zbl0728.60032MR1119989
  5. [5] D. Dehay (1992), Estimation de paramètres fonctionnels spectraux de certains processus non-nécessairement stationnaires, Comptes Rendus de l'Académie des Sciences de Paris, 314 (4), 313-316. Zbl0742.62089MR1151721
  6. [6] D. Dehay (1994), Spectral analysis of the covariance of the almost periodically correlated processes, to appear in Stochastic Process. Appl. Zbl0793.62050MR1273778
  7. [7] D. Dehay and A. Loughani (1994), Locally harmonizable covariances: spectral analysis, to appear in Kybernetika. Zbl0826.60028MR1314350
  8. [8] D. Dehay and R. Moché (1992), Trace measures of a positive definite bimeasure, J. Multivariate Anal.40, 115-131. Zbl0745.60033MR1149255
  9. [9] R. M. Dudley and L. Pakula (1972), A counter example of the inner product of measures, Indiana Univ. Math. J.21, 843-845 Zbl0221.28003MR296245
  10. [10] N. Dunford and J. T. Schwartz (1957), Linear operators, parts I and II: general theory, Interscience Pub. (New York). Zbl0084.10402MR1009162
  11. [11] W. A. Gardner (1985), Introduction to random processes with applications to signals and systems, Macmillan (New York), 2nd ed. 1989McGraw-Hill. Zbl0656.60044
  12. [12] W. A. Gardner (1988), Correlation estimation and time series modeling for nonstationary processes, Signal Processing15, 31-41 MR952544
  13. [13] W. A. Gardner (1994), Cyclostationarity in communications and signal processing, IEEE Press (New York). Zbl0823.00029
  14. [14] E. Gladyshev (1963), Periodically and almost periodically correlated random processes with continuous time parameter, Th. Probability Appl.8, 173-177. Zbl0138.11003MR152005
  15. [15] C. Hipp (1979), Convergence rates of the strong law for stationary mixing sequences, Z. Wahrscheinlichkeitstheorie verw. Gebiete49, 49-62. Zbl0377.60035MR539664
  16. [16] J. E. Huneycutt (1972), Products and convolutions of vector valued set functions, Studia Math.41, 119-129. Zbl0233.28013MR302855
  17. [17] H. L. Hurd (1989), Nonparametric time series analysis for periodically correlated processes, IEEE Transactions on Information Theory IT-35 (2), 350-359. Zbl0672.62096MR999650
  18. [18] H. L. Hurd (1991), Correlation theory for the almost periodically correlated processes with continuous time parameter, J. Multivariate Anal.37 (1), 24-45 Zbl0721.60045MR1097303
  19. [19] H. L. Hurd and Leskow, J. (1992), Estimation of the Fourier coefficient functions and their spectral densities for ɸ-mixing almost periodically correlated processes, Statistics and Probability Letters14 (4), 299-306. Zbl0752.62067MR1179631
  20. [20] H. L. Hurd and J. Leskow (1992), Strongly consistent and asymptotically normal estimation of the covariance for almost periodically correlated processes, Statistics and Decisions10, 201-225 Zbl0757.62045MR1183203
  21. [21] J. Leskow (1992), An asymptotic normality of the spectral density estimators for almost periodically correlated stochatic processes, preprint. Zbl0805.62086MR1290703
  22. [22] M. Peligrad (1992), On the central limit theorem for weakly dependent sequences with a decomposed strong mixing coefficient, Stochastic Process. Appl.42, 181-193 Zbl0757.60028MR1176496
  23. [23] R. S. Phillips (1950), On Fourier Stieltjes integrals, Trans. Amer. Math. Soc.69, 312-323. Zbl0039.33101MR39106
  24. [24] M. M. Rao (1985), Harmonizable, Cramér, and Karhunen classes of processes, Handbook of Statistics5, 279-310, Elsevier Science Publ. MR831752
  25. [25] Yu. A. Rozanov (1959), Spectral analysis of abstract function, Th. Probability Appl.4, 271-287. Zbl0089.32602MR117791

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.