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Probability density estimation from dependent observations using wavelets orthonormal bases

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  • Masry, Elias

Abstract

We consider the estimation of the probability density function [latin small letter f with hook] (x) of stationary mixing processes using wavelet orthonormal bases. For [latin small letter f with hook] belonging to the Sobolev space , we derive precise asymptotic expressions for the mean integrated square estimation error.

Suggested Citation

  • Masry, Elias, 1994. "Probability density estimation from dependent observations using wavelets orthonormal bases," Statistics & Probability Letters, Elsevier, vol. 21(3), pages 181-194, October.
    • Handle: RePEc:eee:stapro:v:21:y:1994:i:3:p:181-194
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    Citations

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    Cited by:

    1. Antonio Cosma & Olivier Scaillet & Rainer von Sachs, 2005. "Multiariate Wavelet-based sahpe preserving estimation for dependant observation," FAME Research Paper Series rp144, International Center for Financial Asset Management and Engineering.
    2. Christophe Chesneau & Isha Dewan & Hassan Doosti, 2012. "Wavelet linear density estimation for associated stratified size-biased sample," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 429-445.
    3. Neumann, Michael H., 1997. "Strong approximation of density estimators from weakly dependent observations by density estimators from independent observations," SFB 373 Discussion Papers 1997,86, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Rodney V. Fonseca & Aluísio Pinheiro, 2020. "Wavelet estimation of the dimensionality of curve time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1175-1204, October.
    5. Gérard, Kerkyacharian & Dominique, Picard, 1997. "Limit of the quadratic risk in density estimation using linear methods," Statistics & Probability Letters, Elsevier, vol. 31(4), pages 299-312, February.
    6. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 97-130, August.
    7. Masry, Elias, 1997. "Multivariate probability density estimation by wavelet methods: Strong consistency and rates for stationary time series," Stochastic Processes and their Applications, Elsevier, vol. 67(2), pages 177-193, May.
    8. Marianna Pensky, 2002. "Locally Adaptive Wavelet Empirical Bayes Estimation of a Location Parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 83-99, March.
    9. Liang Han-Ying & Mammitzsch Volker & Steinebach Josef, 2005. "Nonlinear wavelet density and hazard rate estimation for censored data under dependent observations," Statistics & Risk Modeling, De Gruyter, vol. 23(3/2005), pages 161-180, March.
    10. N. Hosseinioun & H. Doosti & H. Nirumand, 2012. "Nonparametric estimation of the derivatives of a density by the method of wavelet for mixing sequences," Statistical Papers, Springer, vol. 53(1), pages 195-203, February.
    11. García-Treviño, E.S. & Barria, J.A., 2012. "Online wavelet-based density estimation for non-stationary streaming data," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 327-344.

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