IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v130y2019icp111-139.html
   My bibliography  Save this article

The radial wavelet frame density estimator

Author

Listed:
  • García Treviño, E.S.
  • Alarcón Aquino, V.
  • Barria, J.A.

Abstract

The estimation of probability densities is one of the fundamental problems in scientific research. It has been shown that Wavelet Density Estimators, which are a well-documented nonparametric approach, outperform other nonparametric estimators in problems involving densities with discontinuities and local features. However, the use of this type of estimators is not widely extended in the scientific community mainly because of their heavy computational complexity and their difficult algorithmic implementation. A novel multidimensional Wavelet Density Estimator approach based on new multidimensional scaling functions with analytic closed-form expressions is proposed. The key advantages of the proposed estimator are its simpler multidimensional algorithmic implementation and its significant reduction in computational complexity. Algorithmic formulations for four different data analysis scenarios are presented: (1) batch processing of input data, (2) online estimation for stationary process, (3) online estimation for non-stationary contexts and (4) batch estimation of high-dimensional data. The assessment results show that the proposed approach reduces the computational time of the estimation process while maintaining competitive estimation errors.

Suggested Citation

  • García Treviño, E.S. & Alarcón Aquino, V. & Barria, J.A., 2019. "The radial wavelet frame density estimator," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 111-139.
    • Handle: RePEc:eee:csdana:v:130:y:2019:i:c:p:111-139
    DOI: 10.1016/j.csda.2018.08.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318302044
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.08.021?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Caudle, Kyle A. & Wegman, Edward, 2009. "Nonparametric density estimation of streaming data using orthogonal series," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3980-3986, October.
    2. Kerkyacharian, G. & Picard, D., 1992. "Density estimation in Besov spaces," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 15-24, January.
    3. 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.
    4. Pinheiro, Aluisio & Vidakovic, Brani, 1997. "Estimating the square root of a density via compactly supported wavelets," Computational Statistics & Data Analysis, Elsevier, vol. 25(4), pages 399-415, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kirkby, J. Lars & Leitao, Álvaro & Nguyen, Duy, 2021. "Nonparametric density estimation and bandwidth selection with B-spline bases: A novel Galerkin method," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Marina Vannucci & Brani Vidakovic, 1997. "Preventing the Dirac disaster: Wavelet based density estimation," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 145-159, August.
    4. Morettin Pedro A. & Toloi Clelia M.C. & Chiann Chang & de Miranda José C.S., 2011. "Wavelet Estimation of Copulas for Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(3), pages 1-31, October.
    5. Kato, Takeshi, 1999. "Density estimation by truncated wavelet expansion," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 159-168, June.
    6. 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.
    7. 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.
    8. Koo, Ja-Yong & Kim, Woo-Chul, 1996. "Wavelet density estimation by approximation of log-densities," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 271-278, February.
    9. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls," Papers 1201.0224, arXiv.org, revised May 2012.
    10. Federico Palacios-González & Rosa M. García-Fernández, 2020. "A faster algorithm to estimate multiresolution densities," Computational Statistics, Springer, vol. 35(3), pages 1207-1230, September.
    11. Karun Adusumilli & Taisuke Otsu, 2015. "Nonparametric instrumental regression with errors in variables," STICERD - Econometrics Paper Series /2015/585, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    12. Leblanc, Frédérique, 1996. "Wavelet linear density estimator for a discrete-time stochastic process: Lp-losses," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 71-84, March.
    13. 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.
    14. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 97-130, August.
    15. 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.
    16. Durastanti, Claudio, 2016. "Adaptive global thresholding on the sphere," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 110-132.
    17. Naono Ken, 1995. "Comparative Computations of Non-parametric Density Estimation Between Some Kernel Method and the Wavelet Method," Monte Carlo Methods and Applications, De Gruyter, vol. 1(2), pages 147-163, December.
    18. Sultana Didi & Salim Bouzebda, 2022. "Wavelet Density and Regression Estimators for Continuous Time Functional Stationary and Ergodic Processes," Mathematics, MDPI, vol. 10(22), pages 1-37, November.
    19. Zeng, Xiaochen & Wang, Jinru, 2018. "Wavelet density deconvolution estimations with heteroscedastic measurement errors," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 79-85.
    20. Sylvain Sardy & Paul Tseng, 2010. "Density Estimation by Total Variation Penalized Likelihood Driven by the Sparsity ℓ1 Information Criterion," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 321-337, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:130:y:2019:i:c:p:111-139. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.