IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i12p3421-3429.html
   My bibliography  Save this article

Local-moment nonparametric density estimation of pre-binned data

Author

Listed:
  • Papkov, Galen I.
  • Scott, David W.

Abstract

Data-driven research is often hampered by privacy restrictions in the form of limited data sets or graphical representations without the benefit of raw data. Nonparametric techniques that circumvent these issues by using local moment information, thereby extending the piecewise-polynomial histograms, are developed. These methods utilize not only binned data counts, but also their conditional moments in order to better estimate the underlying density of the data. A particular polynomial spline density estimator can be found via penalized least-squares optimization with a roughness penalty. Two issues exist in regards to the original algorithm: (1) local moments for empty bins are undefined and (2) all moment information is treated equally, despite the fact that lower-order moments are more accurate than higher-order moments. Solutions to both issues are provided by using unconditional moments and incorporating a weight matrix into the optimization problem.

Suggested Citation

  • Papkov, Galen I. & Scott, David W., 2010. "Local-moment nonparametric density estimation of pre-binned data," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3421-3429, December.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3421-3429
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00077-0
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. Koo, Ja-Yong & Kooperberg, Charles, 2000. "Logspline density estimation for binned data," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 133-147, January.
    2. Lambert, Philippe & Eilers, Paul H.C., 2009. "Bayesian density estimation from grouped continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1388-1399, February.
    3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, Enero-Abr.
    4. Zhou S. & Shen X., 2001. "Spatially Adaptive Regression Splines and Accurate Knot Selection Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 247-259, March.
    5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, Enero-Abr.
    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. Lambert, Philippe, 2023. "Nonparametric density estimation and risk quantification from tabulated sample moments," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 177-189.

    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. Dimitrova, Dimitrina S. & Kaishev, Vladimir K. & Lattuada, Andrea & Verrall, Richard J., 2023. "Geometrically designed variable knot splines in generalized (non-)linear models," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    2. Maximilian Osterhaus, 2024. "A Sparse Grid Approach for the Nonparametric Estimation of High-Dimensional Random Coefficient Models," Papers 2408.07185, arXiv.org.
    3. Binder, Harald & Sauerbrei, Willi, 2008. "Increasing the usefulness of additive spline models by knot removal," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5305-5318, August.
    4. Yang, Lianqiang & Hong, Yongmiao, 2017. "Adaptive penalized splines for data smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 70-83.
    5. Otto-Sobotka, Fabian & Salvati, Nicola & Ranalli, Maria Giovanna & Kneib, Thomas, 2019. "Adaptive semiparametric M-quantile regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 116-129.
    6. Mestekemper, Thomas & Windmann, Michael & Kauermann, Göran, 2010. "Functional hourly forecasting of water temperature," International Journal of Forecasting, Elsevier, vol. 26(4), pages 684-699, October.
    7. Naschold, Felix, 2012. "“The Poor Stay Poor”: Household Asset Poverty Traps in Rural Semi-Arid India," World Development, Elsevier, vol. 40(10), pages 2033-2043.
    8. Arthur Charpentier & Emmanuel Flachaire & Antoine Ly, 2017. "Econom\'etrie et Machine Learning," Papers 1708.06992, arXiv.org, revised Mar 2018.
    9. Hyunju Son & Youyi Fong, 2021. "Fast grid search and bootstrap‐based inference for continuous two‐phase polynomial regression models," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    10. Welham, S.J. & Thompson, R., 2009. "A note on bimodality in the log-likelihood function for penalized spline mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 920-931, February.
    11. Wei Huang & Oliver Linton & Zheng Zhang, 2022. "A Unified Framework for Specification Tests of Continuous Treatment Effect Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1817-1830, October.
    12. Dlugosz, Stephan & Mammen, Enno & Wilke, Ralf A., 2017. "Generalized partially linear regression with misclassified data and an application to labour market transitions," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 145-159.
    13. Longhi, Christian & Musolesi, Antonio & Baumont, Catherine, 2014. "Modeling structural change in the European metropolitan areas during the process of economic integration," Economic Modelling, Elsevier, vol. 37(C), pages 395-407.
    14. Kuhlenkasper, Torben & Kauermann, Göran, 2010. "Female wage profiles: An additive mixed model approach to employment breaks due to childcare," HWWI Research Papers 2-18, Hamburg Institute of International Economics (HWWI).
    15. Strasak, Alexander M. & Umlauf, Nikolaus & Pfeiffer, Ruth M. & Lang, Stefan, 2011. "Comparing penalized splines and fractional polynomials for flexible modelling of the effects of continuous predictor variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1540-1551, April.
    16. Christian Schluter & Jackline Wahba, 2012. "Abstract: Illegal Migration, Wages, and Remittances: Semi-Parametric Estimation of Illegality Effects," Norface Discussion Paper Series 2012037, Norface Research Programme on Migration, Department of Economics, University College London.
    17. Zi Ye & Giles Hooker & Stephen P. Ellner, 2021. "Generalized Single Index Models and Jensen Effects on Reproduction and Survival," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 492-512, September.
    18. Esra Kürüm & Danh V. Nguyen & Qi Qian & Sudipto Banerjee & Connie M. Rhee & Damla Şentürk, 2024. "Spatiotemporal multilevel joint modeling of longitudinal and survival outcomes in end-stage kidney disease," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(4), pages 827-852, October.
    19. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    20. Carlo Fezzi & Ian Bateman, 2015. "The Impact of Climate Change on Agriculture: Nonlinear Effects and Aggregation Bias in Ricardian Models of Farmland Values," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 2(1), pages 57-92.

    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:54:y:2010:i:12:p:3421-3429. 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.