116
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

On estimating the marginal distribution of a detrended series with long memory

Pages 11539-11557 | Received 29 Nov 2015, Accepted 08 Dec 2016, Published online: 24 Aug 2017

References

  • Beran, J. 1994. Statistics for long-memory processes. New York: Chapman & Hall.
  • Beran, J. 2009. On parametric estimation for locally stationary long-memory processes. Journal of Statistical Planning and Inference 139:900–915.
  • Beran, J., and Y. Feng. 2002. SEMIFAR models: A semiparametric framework for modelling trends, long-range dependence and nonstationarity. Computational Statistics and Data Analysis 40:393–419.
  • Beran, J., Y. Feng, S. Ghosh, and R. Kulik. 2013. Long memory processes: Probabilistic properties and statistical models. Heidelberg: Springer-Verlag.
  • Bierens, H. J. 1983. Uniform consistency of kernel estimators of a regression function under generalized conditions. Journal of American Statistical Association 77:699– 707.
  • Bowman, A. W., and A. Azzalini. 1997. Applied smoothing techniques for data analysis. The kernel approach with S-Plus illustrations. Oxford: Clarenden Press.
  • Breuer, P., and P. Major. 1983. Central limit theorems for nonlinear functionals of Gaussian fields. Journal of Multivariate Analysis 13:425–441.
  • Brohan, P., J. J. Kennedy, I. Harris, S. F. B. Tett, and P. D. Jones 2006. Uncertainty estimates in regional and global observed temperature changes: A new dataset from 1850. Journal of Geophysical Research 111:D12106. doi:10.1029/2005JD006548
  • Csörgő, S. 1980. The empirical moment generating function. In: Colloquia Mathematica Societatis Janos Bolyai, 32, Nonparametric Statistical Inference, Budapest, Ed. I. Vincze, 139–150, North Holland: Amsterdam.
  • Csörgő, S., and J. Mielniczuk. 1995. Nonparametric regression under long-range dependent normal errors. Annals of Statistics 23:1000–1014.
  • Csörgő, S., and J. Mielniczuk. 1996. The empirical process of a short-range dependent stationary sequence under Gaussian subordination. Probability Theory and Related Fields 104:15–25.
  • Dahlhaus, R. 1997. Fitting time series models to nonstationary processes. Annals of Statistics 25:1–37.
  • Dehling, H., and M. S. Taqqu. 1989. The empirical process of some long-range dependent sequences with an application to U-statistics. Annals of Statistics 17:1767–1783.
  • Dobrushin, R. L., and P. Major. 1979. Non-central limit theorems for non-linear functional of Gaussian fields. Probability Theory and Related Fields 50:27–52.
  • Feuerverger, A., and P. McDunnough. 1984. On statistical transform methods and their efficiency. The Canadian Journal of Statistics 12:303–317.
  • Gasser, T., and H. G. Müller. 1984. Estimating regression functions and their derivatives by the kernel method. Scandinavian Journal of Statistics 11:171–185.
  • Geweke, J., and S. Porter-Hudak. 1983. The estimation and application of long memory time series models. Journal of Time Series Analysis 4:221–238.
  • Ghosh, S. 1996. A new graphical tool to detect non-normality. Journal of the Royal Statistical Society, Series B 58:691–702.
  • Ghosh, S. 2001. Nonparametric trend estimation in replicated time series. Journal of Statistical Planning and Inference 97:263–274.
  • Ghosh, S. 2003. Estimating the moment generating function of a linear process. Student 4:211–218.
  • Ghosh, S. 2014. On local slope estimation in partial linear models under Gaussian subordination. Journal of Statistical Planning and Inference 155:42–53.
  • Ghosh, S., and J. Beran. 2000. Comparing two distributions: The two sample T3-plot. Journal of Computational and Graphical Statistics 9:167–179.
  • Ghosh, S., J. Beran. 2006. On estimating the cumulant generating function for linear processes. Annals of the Institute of Statistical Mathematics 58:53–71.
  • Ghosh, S., J. Beran, and J. Innes 1997. Nonparametric conditional quantile estimation in the presence of long memory. Student 2:109–117.
  • Ghosh, S., and D. Draghicescu. 2002. Predicting the distribution function for long-memory processes. International Journal of Forecasting 18:283–290.
  • Guo, H., and H. L. Koul. 2007. Nonparametric regression with heteroscedastic long memory errors. Journal of Statistical Planning and Inference 137:379–404.
  • Hall, P., and J. D. Hart. 1990. Nonparametric regression with long-range dependence. Stochastic Processes and their Applications 36:339–351.
  • Jones, P. D., D. H. Lister, T. J. Osborn, C. Harpham, M. Salmon, and C. P. Morice. 2012. Hemispheric and large-scale land surface air temperature variations: An extensive revision and an update to 2010. Journal of Geophysical Research 117:D05127. doi:10.1029/2011JD017139
  • Kendall, M. G., and A. Stuart. 1963. The advanced theory of statistics, Volume 1, 2nd ed. London: Charles Griffin and Company Limited.
  • Mack, Y. P., and B. W. Silverman. 1982. Weak and strong uniform consistency of kernel regression estimates. Probability Theory and Related Fields 61:405–415.
  • Major, P. 1981. Limit theorems for non-linear functionals of Gaussian sequences. Probability Theory and Related Fields 57:129–158.
  • Meintanis, S. G. 2007. A Kolmogorov-Smirnov type test for skew normal distributions based on the empirical moment generating function. Journal of Statistical Planning and Inference 137:2681–2688.
  • Menéndez, P., S. Ghosh, H. R. Künsch, and W. Tinner. 2013. On trend estimation under monotone Gaussian subordination with long-memory: Application to fossil pollen series. Journal of Nonparametric Statistics 25:765–785.
  • Parzen, E. 1962. On estimation of a probability density function and mode. The Annals of Mathematical Statistics 33:1065–1076.
  • Priestley, M. B., and M. T. Chao. 1972. Nonparametric function fitting. Journal of the Royal Statistical Society, Series B 34:385–392.
  • Ray, B. K., and R. Tsay. 1997. Bandwidth selection for kernel regression with long-range dependent errors. Biometrika 84:791–802.
  • Rice, J. 1986. Convergence rates for partially splined models. Statistics and Probability Letters 4:203–208.
  • Robinson, P. M. 1997. Large-sample inference for nonparametric regression with dependent errors. Annals of Statistics 25:2054–2083.
  • Robinson, P. M., and F. J. Hidalgo. 1997. Time series regression with long-range dependence. Annals of Statistics 25:77–104.
  • Rosenblatt, M. 1956. Remarks on some nonparametric estimates of a density function. Annals of Mathematical Statistics 27:832–835.
  • Rosenblatt, M. 1971. Curve estimates. Annals of Statistics 42:1815–1842.
  • Scott, D. W. 1979. On optimal and data-based histograms. Biometrika 66:605–610.
  • Scott, D. W. 1992. Multivariate density estimation: Theory, practice, and visualization. New York: Wiley.
  • Silverman, B. W. 1978. Weak and strong uniform consistency of kernel estimate of a density and its derivative. Annals of Statistics 6:177–184.
  • Silverman, B. W. 1986. Density estimation. New York: Chapman & Hall.
  • Speckman, P. 1988. Kernel smoothing in partial linear models. Journal of the Royal Statistical Society, Series B 50:413–436.
  • Taqqu, M. S. 1975. Weak convergence to fractional Brownian motion and to the Rosenblatt process. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 31:287–302.
  • Wand, M. P., and M. C. Jones. 1995. Kernel smoothing. London: Chapman & Hall.

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.