IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2017-69.html

Some searches may not work properly. We apologize for the inconvenience.

   My bibliography  Save this paper

A note on the adaptive estimation of the di?erential entropy by wavelet methods

Author

Listed:
  • Christophe Chesneau

    (Université de Caen; LMNO)

  • Fabien Navarro

    (CREST;ENSAI)

  • Oana Silvia Serea

    (Université Perpignan; Laboratoire de Mathématiques et Physique)

Abstract

In this note we consider the estimation of the di?erential entropy of a probability density function. We propose a new adaptive estimator based on a plug-in approach and wavelet methods. Under the mean Lp error, p = 1, this estimator attains fast rates of convergence for a wide class of functions. We present simulation results in order to support our theoretical ?ndings.

Suggested Citation

  • Christophe Chesneau & Fabien Navarro & Oana Silvia Serea, 2017. "A note on the adaptive estimation of the di?erential entropy by wavelet methods," Working Papers 2017-69, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2017-69
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2017-69.pdf
    File Function: CREST working paper version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 97-130, August.
    2. Harry Joe, 1989. "Estimation of entropy and other functionals of a multivariate density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(4), pages 683-697, December.
    Full references (including those not matched with items on IDEAS)

    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. Emmanouil Androulakis & Christos Koukouvinos & Kalliopi Mylona & Filia Vonta, 2010. "A real survival analysis application via variable selection methods for Cox's proportional hazards model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(8), pages 1399-1406.
    2. E. Androulakis & C. Koukouvinos, 2013. "A new variable selection method for uniform designs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2564-2578, December.
    3. A. Karagrigoriou & C. Koukouvinos & K. Mylona, 2010. "On the advantages of the non-concave penalized likelihood model selection method with minimum prediction errors in large-scale medical studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(1), pages 13-24.
    4. Xingwei Tong & Xin He & Liuquan Sun & Jianguo Sun, 2009. "Variable Selection for Panel Count Data via Non‐Concave Penalized Estimating Function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 620-635, December.
    5. Ertefaie Ashkan & Asgharian Masoud & Stephens David A., 2018. "Variable Selection in Causal Inference using a Simultaneous Penalization Method," Journal of Causal Inference, De Gruyter, vol. 6(1), pages 1-16, March.
    6. Ashis K. Gangopadhyay & Robert disario & Dipak K. Dey, 1997. "A nonparametric approach to k-sample inference based on entropy-super-," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 8(3), pages 237-252, September.
    7. Christophe Chesneau & Fabien Navarro, 2017. "On the pointwise mean squared error of a multidimensional term-by-term thresholding wavelet estimator," Working Papers 2017-68, Center for Research in Economics and Statistics.
    8. Yongmiao Hong & Xia Wang & Wenjie Zhang & Shouyang Wang, 2017. "An efficient integrated nonparametric entropy estimator of serial dependence," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 728-780, October.
    9. Abbaszadeh, Mohammad & Chesneau, Christophe & Doosti, Hassan, 2012. "Nonparametric estimation of density under bias and multiplicative censoring via wavelet methods," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 932-941.
    10. Yu, Xiufan & Yao, Jiawei & Xue, Lingzhou, 2024. "Power enhancement for testing multi-factor asset pricing models via Fisher’s method," Journal of Econometrics, Elsevier, vol. 239(2).
    11. Felix Abramovich & Claudia Angelini & Daniela Canditiis, 2007. "Pointwise optimality of Bayesian wavelet estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(3), pages 425-434, September.
    12. Jan G. De Gooijer & Ao Yuan, 2008. "MDL Mean Function Selection in Semiparametric Kernel Regression Models," Tinbergen Institute Discussion Papers 08-046/4, Tinbergen Institute.
    13. Liu-Cang Wu & Zhong-Zhan Zhang & Deng-Ke Xu, 2012. "Variable selection in joint mean and variance models of Box--Cox transformation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(12), pages 2543-2555, August.
    14. Yao Dong & He Jiang, 2018. "A Two-Stage Regularization Method for Variable Selection and Forecasting in High-Order Interaction Model," Complexity, Hindawi, vol. 2018, pages 1-12, November.
    15. Cui, Jingyu & Yi, Grace Y., 2024. "Variable selection in multivariate regression models with measurement error in covariates," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    16. Herrera Gómez, Marcos, 2010. "Causalidad Espacial. Enfoque No Paramétrico [Spatial Causality. Non-Parametric Approach]," MPRA Paper 61326, University Library of Munich, Germany.
    17. Christophe Chesneau, 2014. "A Note on Wavelet Estimation of the Derivatives of a Regression Function in a Random Design Setting," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-8, April.
    18. Abramovich, Felix & Besbeas, Panagiotis & Sapatinas, Theofanis, 2002. "Empirical Bayes approach to block wavelet function estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 435-451, June.
    19. Kojadinovic, Ivan, 2005. "Relevance measures for subset variable selection in regression problems based on k-additive mutual information," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1205-1227, June.
    20. Zhang, Jing & Wang, Qin & Mays, D'Arcy, 2021. "Robust MAVE through nonconvex penalized regression," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).

    More about this item

    Keywords

    Entropy; Wavelet estimation; Rate of convergence; Mean Lp error;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:crs:wpaper:2017-69. 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: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

    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.