272
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Two-sample U-statistic processes for long-range dependent data

, &
Pages 84-104 | Received 29 Sep 2016, Accepted 29 Sep 2016, Published online: 13 Jan 2017

References

  • Csörgő M, Horváth L. Invariance principles for change-point problems. J Multivariate Anal. 1988;27:151–168. doi: 10.1016/0047-259X(88)90122-4
  • Dehling H, Fried R, Garcia I, Wendler M. Change-point detection under dependence based on two-sample U-statistics. In: Dawson D et al., editors. Asymptotic laws and methods in stochastics: Fields institute communications 76. New York: Springer; 2015. p. 195–220.
  • Csörgő M, Horváth L. Limit theorems in change-point analysis. New York: J. Wiley & Sons; 1997.
  • Horváth L, Kokoszka P. The effect of long-range dependence on change-point estimators. J Statist Plann Inference. 1997;64:57–81. doi: 10.1016/S0378-3758(96)00208-X
  • Dehling H, Rooch A, Taqqu MS. Non-parametric change-point tests for long-range dependent data. Scand J Statist. 2013;40:153–173. doi: 10.1111/j.1467-9469.2012.00799.x
  • Horváth L, Shao Q-M. Limit theorem for maximum of standardized U-statistics with an application. Ann Statist. 1996;24:2266–2279. doi: 10.1214/aos/1069362321
  • Horváth L, Shao Q-M. Darling-Erdős-type theorems for sums of Gaussian variables with long-range dependence. Stochastic Process Appl. 1996;63:117–137. doi: 10.1016/0304-4149(96)00053-1
  • Mandelbrot BB, Wallis JR. Noah, Joseph and operational hydrology. Water Res Res. 1968;4:909–918. doi: 10.1029/WR004i005p00909
  • Caballero R, Jewson S, Brix A. Long memory in surface air temperature: detection, modeling, and application to weather derivative valuation. Climate Res. 2002;21:127–140. doi: 10.3354/cr021127
  • Levy JB, Taqqu MS. Renewal reward processes with heavy-tailed inter-renewal times and heavy-tailed rewards. Bernoulli. 2000;6:23–44. doi: 10.2307/3318631
  • Willinger W, Taqqu MS, Erramilli A. A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks. In: Kelly FP, Zachary S, Ziedins I, editors. Stochastic networks: theory and applications. Oxford: Clarendon Press; 1996. p. 339–366.
  • Cappé O, Moulines E, Pesquet J-C, Petropulu A, Yang X. Long-range dependence and heavy-tail modeling for teletraffic data. IEEE Signal Process Mag. 2002;19:14–27. doi: 10.1109/79.998079
  • Lo AW. Long-term memory in stock market prices. Econometrica. 1991;59:1279–1313. doi: 10.2307/2938368
  • Breidt FJ, Crato N, de Lima P. The detection and estimation of long memory in stochastic volatility. J Econometrics. 1998;83:325–348. doi: 10.1016/S0304-4076(97)00072-9
  • Willinger W, Taqqu MS, Teverovsky V. Stock market prices and long-range dependence. Finance Stoch. 1999;3:1–13. doi: 10.1007/s007800050049
  • Baillie RT. Long memory processes and fractional integration in econometrics. J Econometrics. 1996;73:5–59. doi: 10.1016/0304-4076(95)01732-1
  • Doukhan P, Oppenheim G, Taqqu MS, editors. Theory and applications of long-range dependence. Basel: Birkhäuser; 2003.
  • Beran J. Long-range dependence. Comput Statist. 2010;2:26–35. doi: 10.1002/wics.52
  • Dehling H, Taqqu MS. The empirical process of some long-range dependent sequences with an application to U-statistics. Ann Statist. 1989;17:1767–1783. doi: 10.1214/aos/1176347394
  • Dehling H, Taqqu MS. Bivariate symmetric statistics of long-range dependent observations. J Statist Plann Inference. 1991;28:153–165. doi: 10.1016/0378-3758(91)90023-8
  • Lévy-Leduc C, Boistard H, Moulines E, Taqqu MS, Reisen VA. Asymptotic properties of U-processes under long-range dependence. Ann Statist. 2011;39:1399–1426. doi: 10.1214/10-AOS867
  • Dobrushin RL, Major P. Non-central limit theorems for non-linear functional of Gaussian fields. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete. 1979;50:27–52. doi: 10.1007/BF00535673
  • Taqqu MS. Convergence of integrated processes of arbitrary Hermite rank. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete. 1979;50:53–83. doi: 10.1007/BF00535674
  • Taqqu MS. Weak convergence to fractional Brownian motion and to the Rosenblatt process. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete. 1975;31:287–302. doi: 10.1007/BF00532868
  • Beran J, Feng Y, Ghosh S, Kulik R. Long-memory processes. Heidelberg: Springer Verlag; 2013.
  • Pipiras V, Taqqu MS. Long range dependence and self-similarity. Cambridge University Press. Forthcoming.
  • Lévy-Leduc C, Taqqu MS. Hermite ranks and U-statistics. Metrika. 2014;77:105–136. doi: 10.1007/s00184-013-0474-4
  • Major P. Limit theorems for non-linear functionals of Gaussian sequences. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete. 1981;57:129–158. doi: 10.1007/BF00533717
  • Major P. Multiple Wiener-Itô integrals. Lecture Notes in Mathematics 849. Berlin, Heidelberg: Springer; 1981. doi: 10.1007/BFb0094036
  • Leucht A, Neumann MH. Dependent wild bootstrap for degenerate U- and V-statistics. J Multivariate Anal. 2013;117:257–280. doi: 10.1016/j.jmva.2013.03.003
  • Denker M, Gordin M. Limit theorems for von Mises statistics of a measure preserving transformation. Probab Theory Related Fields. 2014;160:1–45. doi: 10.1007/s00440-013-0522-z
  • Beutner E, Zähle H. Deriving the asymptotic distribution of U- and V-statistics of dependent data using weighted empirical processes. Bernoulli. 2012;18:803–822. doi: 10.3150/11-BEJ358
  • Gradshteyn IS, Ryzhik IM. Table of integrals, series and products. New York: Academic Press; 1980.
  • Huber PJ. Robust statistics. New York: John Wiley and Sons; 1981.
  • Móricz F. Moment inequalities and the strong laws of large numbers. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete. 1976;35:299–314. doi: 10.1007/BF00532956
  • Bai S, Taqqu MS. Multivariate limit theorems in the context of long-range dependence. J Time Ser Anal. 2013;34:717–743. doi: 10.1111/jtsa.12046
  • Shorack GR, Wellner JA. Empirical processes with applications to statistics. New York: John Wiley & Sons; 1986.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.