IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v115y2013icp138-156.html
   My bibliography  Save this article

The dictionary approach for spherical deconvolution

Author

Listed:
  • Pham Ngoc, Thanh Mai
  • Rivoirard, Vincent

Abstract

We consider the problem of estimating a density of probability from indirect data in the spherical convolution model. We aim at building an estimate of the unknown density as a linear combination of functions of an overcomplete dictionary. The procedure is devised through a well-calibrated ℓ1-penalized criterion. The spherical deconvolution setting has been barely studied so far, and the two main approaches to this problem, namely the SVD and the hard thresholding ones considered only one basis at a time. The dictionary approach allows to combine various bases and thus enhances estimates sparsity. We provide an oracle inequality under global coherence assumptions. Moreover, the calibrated procedure that we put forward gives quite satisfying results in the numerical study when compared with other procedures.

Suggested Citation

  • Pham Ngoc, Thanh Mai & Rivoirard, Vincent, 2013. "The dictionary approach for spherical deconvolution," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 138-156.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:138-156
    DOI: 10.1016/j.jmva.2012.08.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12002096
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2012.08.011?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. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Kim, Peter T. & Koo, Ja-Yong & Park, Heon Jin, 2004. "Sharp minimaxity and spherical deconvolution for super-smooth error distributions," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 384-392, August.
    3. Kim, Peter T. & Koo, Ja-Yong, 2002. "Optimal Spherical Deconvolution," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 21-42, January.
    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. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    2. Kim, Peter T. & Koo, Ja-Yong & Luo, Zhi-Ming, 2009. "Weyl eigenvalue asymptotics and sharp adaptation on vector bundles," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1962-1978, October.
    3. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    4. Xu, Yang & Zhao, Shishun & Hu, Tao & Sun, Jianguo, 2021. "Variable selection for generalized odds rate mixture cure models with interval-censored failure time data," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    5. 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.
    6. Li, Chunyu & Lou, Chenxin & Luo, Dan & Xing, Kai, 2021. "Chinese corporate distress prediction using LASSO: The role of earnings management," International Review of Financial Analysis, Elsevier, vol. 76(C).
    7. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.
    8. Yanlin Tang & Xinyuan Song & Zhongyi Zhu, 2015. "Variable selection via composite quantile regression with dependent errors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(1), pages 1-20, February.
    9. Gustavo Peralta, 2016. "The Nature of Volatility Spillovers across the International Capital Markets," CNMV Working Papers CNMV Working Papers no. 6, CNMV- Spanish Securities Markets Commission - Research and Statistics Department.
    10. Bakalli, Gaetan & Guerrier, Stéphane & Scaillet, Olivier, 2023. "A penalized two-pass regression to predict stock returns with time-varying risk premia," Journal of Econometrics, Elsevier, vol. 237(2).
    11. Chuliá, Helena & Garrón, Ignacio & Uribe, Jorge M., 2024. "Daily growth at risk: Financial or real drivers? The answer is not always the same," International Journal of Forecasting, Elsevier, vol. 40(2), pages 762-776.
    12. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2022. "How is machine learning useful for macroeconomic forecasting?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 920-964, August.
    13. Wongsa-art, Pipat & Kim, Namhyun & Xia, Yingcun & Moscone, Francesco, 2024. "Varying coefficient panel data models and methods under correlated error components: Application to disparities in mental health services in England," Regional Science and Urban Economics, Elsevier, vol. 106(C).
    14. Andrea Bucci, 2020. "Realized Volatility Forecasting with Neural Networks," Journal of Financial Econometrics, Oxford University Press, vol. 18(3), pages 502-531.
    15. Christopher J Greenwood & George J Youssef & Primrose Letcher & Jacqui A Macdonald & Lauryn J Hagg & Ann Sanson & Jenn Mcintosh & Delyse M Hutchinson & John W Toumbourou & Matthew Fuller-Tyszkiewicz &, 2020. "A comparison of penalised regression methods for informing the selection of predictive markers," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-14, November.
    16. Jun Zhu & Hsin‐Cheng Huang & Perla E. Reyes, 2010. "On selection of spatial linear models for lattice data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 389-402, June.
    17. Jammalamadaka, S. Rao & Terdik, György H., 2019. "Harmonic analysis and distribution-free inference for spherical distributions," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 436-451.
    18. Norman R. Swanson & Weiqi Xiong, 2018. "Big data analytics in economics: What have we learned so far, and where should we go from here?," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 51(3), pages 695-746, August.
    19. Dong, C. & Li, S., 2021. "Specification Lasso and an Application in Financial Markets," Cambridge Working Papers in Economics 2139, Faculty of Economics, University of Cambridge.
    20. Lam, Clifford, 2008. "Estimation of large precision matrices through block penalization," LSE Research Online Documents on Economics 31543, London School of Economics and Political Science, LSE Library.

    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:jmvana:v:115:y:2013:i:c:p:138-156. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.