Publication Cover
Statistics
A Journal of Theoretical and Applied Statistics
Volume 48, 2014 - Issue 1
259
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Ratio tests for variance change in nonparametric regression

&
Pages 1-16 | Received 07 Jul 2010, Accepted 27 Jun 2012, Published online: 30 Jul 2012

References

  • D.A. Hsu, Tests for variance shift at an unknown time point, Appl. Stat. 26 (1977), pp. 279–284. doi: 10.2307/2346968
  • C. Inclán and G.C. Tiao, Use of cumulative sums of squares for retrospective detection of changes of variances, J. Am. Statist. Assoc. 89 (1994), pp. 913–923.
  • E. Gombay, L. Horváth, and M. Hušková, Estimators and tests for change in variances, Stat. Decis. 14 (1996), pp. 145–159.
  • M. Csörgó and L. Horváth, Limit Theorems in Change-Point Analysis, Wiley, Chichester, 1997.
  • S. Lee and S. Park, The cusum of squares test for scale changes in infinite order moving average processes, Scand. J. Stat. 28 (2001), pp. 625–644. doi: 10.1111/1467-9469.00259
  • S. Lee, O. Na, and S. Na, On the cusum of squares test for variance change in nonstationary and nonparametric time series models, Ann. Inst. Statist. Math. 55 (2003), pp. 467–485. doi: 10.1007/BF02517801
  • Z. Chen and Z. Tian, Modified procedures for change point monitoring in linear models, Math. Comput. Simul. 81 (2010), pp. 62–75. doi: 10.1016/j.matcom.2010.06.021
  • Z. Chen, Z. Tian, and R. Qin, Monitoring variance change in infinite order moving average processes and nonstationary autoregressive processes, Comm. Stat. Theory Methods 40 (2011), pp. 1254–1270. doi: 10.1080/03610920903576564
  • P. Hall and J.D. Hart, Nonparametric regression with long range dependence, Stochastic Process. Appl. 36 (1990), pp. 339–351. doi: 10.1016/0304-4149(90)90100-7
  • J. Fan and I. Gijbels, Local Polynomial Theory and Its Applications, Chapman and Hall, London, 1996.
  • Y.K. Lee, E. Mammen, and B.U. Park, Bandwidth selection for kernel regression with correlation errors, Statistics 44 (2010), pp. 327–340. doi: 10.1080/02331880903138452
  • H.G. Müller, Change-points in nonparametric regression analysis, Ann. Stat. 24 (1992), pp. 1667–1678.
  • M.A. Delgado and J. Hidalgo, Nonparametric inference on structural breaks, J. Econom. 96 (2000), pp. 113–144. doi: 10.1016/S0304-4076(99)00052-4
  • L. Horváth and P. Kokoszka, Change point detection with nonparametric regression, Statistics 36 (2002), pp. 9–31. doi: 10.1080/02331880210930
  • C. Prieur, Change point estimation by local linear smoothing under a weak dependence condition, Math. Methods Stat. 16 (2007), pp. 25–41. doi: 10.3103/S1066530707010036
  • I. Gijbels and A.C. Goderniaus, atBootstrap test for change-points in nonparametric regression, J. Nonparametr. Stat. 16 (2004), pp. 591–611. doi: 10.1080/10485250310001626088
  • L. Su and Z. Xiao, Testing structural change in time-series nonparametric regression models, Stat. Inference 1 (2008), pp. 347–366.
  • Y. Wang, Jump and sharp cusp detection by wavelets, Biometrika 82 (1995), pp. 385–397. doi: 10.1093/biomet/82.2.385
  • M. Raimondo and N. Tajvidi, A peaks over threshold model for change-point detection by wavelets, Statist. Sinica 14 (2004), pp. 395–412.
  • G. Chen, Y.K. Choi, and Y. Zhou, Detection of changes in return by a wavelet smoother with conditional heteroscedastic volatility, J. Econom. 143 (2008), pp. 227–262. doi: 10.1016/j.jeconom.2007.10.001
  • N. Neumeyer and V. Keilegon, Change-point tests for the error distribution in nonparametric regression, Scand. J. Stat. 36 (2009), pp. 518–541. doi: 10.1111/j.1467-9469.2009.00639.x
  • G. Chen, Y.K. Choi, and Y. Zhou, Nonparametric estimation of structural change points in volatility models for time series, J. Econom. 126 (2005), pp. 79–114. doi: 10.1016/j.jeconom.2004.02.008
  • L. Horváth, Z. Horváth, and M. Hušková, Ratio tests for change point detection, Inst. Math. Stat. 1 (2008), pp. 293–304.
  • J. Opsomer, Y. Wang, and Y. Yang, Nonparametric regression with correlated errors, Statist. Sci. 16 (2001), pp. 134–153. doi: 10.1214/ss/1009213287
  • D. Ruppert, M.P. Wand, and R.J. Carroll, Semiparametric Regression, Cambridge University Press, Cambridge, 2003.
  • P. Doukhan, Mixing: Properties and Example, Lecture Notes in Statistics, Springer-Verlag, New York, 1994.

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.