44
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Evaluation of threshold selection methods for adaptive wavelet quantile density estimation in the presence of bias

& ORCID Icon
Received 24 Jan 2023, Accepted 29 Jul 2023, Published online: 14 Aug 2023

References

  • Ahmad, I. A. 1995. On multivariate kernel estimation for samples from weighted distributions. Statistics & Probability Letters 22 (2):121–9. doi:10.1016/0167-7152(94)00057-F.
  • Akbari, M., M. Rezaei, S. Jomhoori, and V. Fakoor. 2019. Nonparametric estimators for quantile density function under length-biased sampling. Communications in Statistics - Theory and Methods 48 (19):4918–35. doi:10.1080/03610926.2018.1549245.
  • Antoniadis, A. 1997. Wavelets in statistics: A review (with discussion). Journal of the Italian Statistical Society 6 (2):97–130. doi:10.1007/BF03178905.
  • Cai, T. 1999. Adaptive wavelet estimation: A block thresholding and oracle inequality approach. The Annals of Statistics 27 (3):898–924. doi:10.1214/aos/1018031262.
  • Cai, T. 2002. On block thresholding in wavelet regression: Adaptivity, block size and threshold level. Statistica Sinica 12:1241–73.
  • Cai, T., and B. W. Silverman. 2001. Incorporating information on neighboring coefficients into wavelet estimation. Sankhya Series B 63:127–48.
  • Cheng, C. 2002. Almost-sure uniform error bounds of general smooth estimators of quantile density functions. Statistics & Probability Letters 59 (2):183–94. doi:10.1016/S0167-7152(02)00160-8.
  • Chesneau, C. 2010. Wavelet block thresholding for density estimation in the presence of bias. Journal of the Korean Statistical Society 39 (1):43–53. doi:10.1016/j.jkss.2009.03.004.
  • Chesneau, C., I. Dewan, and H. Doosti. 2016. Nonparametric estimation of a quantile density function by wavelet methods. Computational Statistics and Data Analysis 94:161–74. doi:10.1016/j.csda.2015.08.006.
  • Cox, D. R. Jr. 1969. Some sampling problems in technology, new developments in survey sampling, eds. N. L. Johnson and H. Smith, 506–27. New York: Wiley-Interscience.
  • Daubechies, I. 1992. Ten lectures on wavelets. CBMS-NSF regional conferences series in applied mathematics. Philadelphia: SIAM.
  • Donoho, D. L., and I. M. Johnstone. 1994. Ideal spatial adaptation via wavelet shrinkage. Biometrika 81 (3):425–55. doi:10.1093/biomet/81.3.425.
  • Donoho, D. L., I. M. Johnstone, G. Kerkyacharian, and D. Picard. 1996. Density estimation by wavelet thresholding. Annals of Statistics 24:508–39.
  • Hall, P., G. Kerkyacharian, and D. Picard. 1999. On the minimax optimality of block thresholded wavelet estimators.Statist. Sinica 9:33–50.
  • Hardle, W., G. Kerkyacharian, D. Picard, and A. Tsybakov. 1998. Wavelet, approximation and statistical applications. Lectures notes in statistics. New York: Springer Verlag.
  • Jin, Q. 2017. Biased sampling, over-identified parameter problems and beyond. Singapore: Springer. doi:10.1007/978-981-10-4856-2.
  • Jones, M. C. 1992. Estimating densities, quantiles, quantile densities and density quantiles. Annals of the Institute of Statistical Mathematics 44 (4):721–7. doi:10.1007/BF00053400.
  • Kerkyacharian, G., and D. Picard. 2004. Regression in random design and warped wavelets. Bernoulli 10 (6):1053–105. doi:10.3150/bj/1106314850.
  • Lawless, J. F. 2003. Statistical models and methods for lifetime data, 2nd ed., 69–70. New York: John Wiley and Sons.
  • Meyer, Y. 1992. Wavelets and operators. Cambridge: Cambridge University Press.
  • Muttlak, H. A., and L. L. McDonald. 1990. Ranked set sampling with size-biased probability of selection. Biometrics 46 (2):435–45. doi:10.2307/2531448.
  • Parzen, E. 1979. Non parametric statistical data modeling. Journal of American Statistical Association 74 (365):105–21. doi:10.1080/01621459.1979.10481621.
  • Shirazi, E., and H. Doosti. 2008. Estimation Of the survival function for m-dependent random varible. Far East Journal of Theoretical Statistics 25 (1):135–44.
  • Shirazi, E., and H. Doosti. 2015. Multivariate wavelet-based density estimation with size-biased data. Statistical Methodology 27:12–9. doi:10.1016/j.stamet.2015.05.002.
  • Shirazi, E., and H. Doosti. 2022. Nonparametric estimation of a quantile density function under Lp risk via block thresholding method. Communications in Statistics - Simulation and Computation 51 (2):539–53. doi:10.1080/03610918.2019.1656250.
  • Shirazi, E., H. Doosti, H. A. Niroumand, and N. Hosseinioun. 2013. Nonparametric regression estimates with censored data based on block thresholding method. Journal of Statistical Planning and Inference 143 (7):1150–65. doi:10.1016/j.jspi.2013.01.003.
  • Soni, P., I. Dewan, and K. Jain. 2012. Nonparametric estimation of quantile density function. Computational Statistics and Data Analysis 56 (12):3876–86. doi:10.1016/j.csda.2012.04.014.
  • Tukey, J. W. 1965. Which part of the sample contains the information? Proceedings of the National Academy of Sciences of the United States of America 53 (1):127–34. doi:10.1073/pnas.53.1.127.
  • Vardi, Y. 1982a. Nonparametric estimation in presence of length bias. Annals of Statistics 10:616–20.
  • Vardi, Y. 1982b. Nonparametric estimation in renewal processes. The Annals of Statistics 10 (3):772–85. doi:10.1214/aos/1176345870.
  • Xiang, X. 1994. A law ofthe logarithm for kernel quantile density estimators. The Annals of Probability 22 (2):1078–91. doi:10.1214/aop/1176988741.
  • Zhou, Y., and S. F. Y. Paul. 1999. Nonparametric estimation of quantile density function for truncated and censored data. Journal of Nonparametric Statistics 12 (1):17–39. doi:10.1080/10485259908832796.

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.