Asymptotics of weighted empirical processes of linear fields with long-range dependence

Paul Doukhan; Gabriel Lang; Donatas Surgailis

Annales de l'I.H.P. Probabilités et statistiques (2002)

  • Volume: 38, Issue: 6, page 879-896
  • ISSN: 0246-0203

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Doukhan, Paul, Lang, Gabriel, and Surgailis, Donatas. "Asymptotics of weighted empirical processes of linear fields with long-range dependence." Annales de l'I.H.P. Probabilités et statistiques 38.6 (2002): 879-896. <http://eudml.org/doc/77746>.

@article{Doukhan2002,
author = {Doukhan, Paul, Lang, Gabriel, Surgailis, Donatas},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {linear random fields; long-range dependence},
language = {eng},
number = {6},
pages = {879-896},
publisher = {Elsevier},
title = {Asymptotics of weighted empirical processes of linear fields with long-range dependence},
url = {http://eudml.org/doc/77746},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Doukhan, Paul
AU - Lang, Gabriel
AU - Surgailis, Donatas
TI - Asymptotics of weighted empirical processes of linear fields with long-range dependence
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2002
PB - Elsevier
VL - 38
IS - 6
SP - 879
EP - 896
LA - eng
KW - linear random fields; long-range dependence
UR - http://eudml.org/doc/77746
ER -

References

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  1. [1] S. Albeverio, S.A. Molchanov, D. Surgailis, Stratified structure of the Universe and Burgers' equation – a probabilistic approach, Probab. Theory Related Fields100 (1994) 457-484. Zbl0810.60058
  2. [2] V.V. Anh, J.M. Angulo, M.D. Ruiz-Medina, Possible long-range dependence in fractional random fields, J. Statist. Plan. Inf.80 (1999) 95-110. Zbl1039.62090MR1713795
  3. [3] H. Dehling, M.S. Taqqu, The empirical process of some long-range dependent sequences with an application to U-statistics, Ann. Statist.17 (1989) 1767-1783. Zbl0696.60032MR1026312
  4. [4] M. Denker, Weak convergence in nonparametric statistics, in: Bhattacharya R., Denker M. (Eds.), Asymptotic Statistics, Birkhäuser, 1990. 
  5. [5] R.L. Dobrushin, P. Major, Non-central limit theorems for non-linear functions of Gaussian fields, Z. Wahrsch. Verw. Geb.50 (1979) 27-52. Zbl0397.60034MR550122
  6. [6] P. Doukhan, D. Surgailis, Functional central limit theorem for the empirical process of short memory linear processes, C. R. Acad. Sci. Paris Serie 1326 (1998) 87-92. Zbl0948.60012MR1649521
  7. [7] L. Giraitis, H.L. Koul, D. Surgailis, Asymptotic normality of regression estimators with long memory errors, Statist. Probab. Lett.29 (1996) 317-335. Zbl0903.62022MR1409327
  8. [8] L. Giraitis, D. Surgailis, Central limit theorem for the empirical process of a linear sequence with long memory, J. Stat. Plan. Inf.80 (1999) 81-93. Zbl0943.60035MR1713796
  9. [9] H.C. Ho, T. Hsing, On the asymptotic expansion of the empirical process of long memory moving averages, Ann. Statist.24 (1996) 992-1024. Zbl0862.60026MR1401834
  10. [10] H.C. Ho, T. Hsing, Limit theorems for functionals of moving averages, Ann. Probab.25 (1997) 1636-1669. Zbl0903.60018MR1487431
  11. [11] A.V. Ivanov, N.N. Leonenko, Statistical Analysis of Random Fields, Kluwer, Dordrecht, 1989. Zbl0713.62094MR1009786
  12. [12] H.L. Koul, Weighted Empiricals and Linear Models, IMS Lecture Notes-Monograph Series, 21, Hayward, CA, 1992. Zbl0998.62501MR1218395
  13. [13] H.L. Koul, K. Mukherjee, Asymptotics of R-, MD- and LAD-estimators in linear regression models with long range dependent errors, Probab. Theory Related Fields95 (1993) 535-553. Zbl0794.60020MR1217450
  14. [14] H.L. Koul, D. Surgailis, Asymptotic expansion of M-estimators with long memory errors, Ann. Statist.25 (1997) 818-850. Zbl0885.62101MR1439325
  15. [15] H.L. Koul, D. Surgailis, Asymptotics of empirical processes of long memory moving averages with infinite variance, Stoch. Proc. Appl.91 (2001) 309-336. Zbl1046.62089MR1807679
  16. [16] N.N. Leonenko, Random Fields with Singular Spectrum, Kluwer, Dordrecht, 1999. Zbl0963.60048
  17. [17] N.N. Leonenko, W.A. Woyczynski, Parameter identification for singular random fields arising in Burgers' turbulence, J. Statist. Plan. Inf.80 (1999) 1-14. Zbl0986.62077MR1713800
  18. [18] D. Marinucci, Gaussian semiparametric estimation for random fields with singular spectrum, Preprint, 2001. MR2030243
  19. [19] D. Surgailis, W.A. Woyczynski, Scaling limits of solutions of Burgers' equation with singular Gaussian initial data, in: Houdré C., Pérez-Abreu V. (Eds.), Chaos Expansions, Multiple Wiener–Itô Integrals and Their Applications, CRC Press, Boca Raton, 1994, pp. 145-162. Zbl0849.35122
  20. [20] M.S. Taqqu, Convergence of integrated processes of arbitrary Hermite rank, Z. Wahrsch. Verw. Geb.50 (1979) 53-83. Zbl0397.60028MR550123

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