IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/10437.html
   My bibliography  Save this paper

Nonparametric estimation of a mixing density via the kernel method

Author

Listed:
  • Goutis, Constantinos

Abstract

We present a method to estimate the latent distribution for a mixture model. Our method is motivated by the standard kernel density estimation but instead of using an estimate based on the unobserved latent variables, we take the expectation with respect to their distribution conditional on the data. The resulting estimator is continuous and, hence, is appropriate when there is a strong belief in the continuity of the mixing distribution. We present an asymptotic justification and we discuss the associated computational problems. The method is illustrated by an example of fission track analysis where we estimate the densi ty of the age of crystals.

Suggested Citation

  • Goutis, Constantinos, 1996. "Nonparametric estimation of a mixing density via the kernel method," DES - Working Papers. Statistics and Econometrics. WS 10437, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:10437
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/bitstream/handle/10016/10437/ws9630.pdf?sequence=1
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Goutis, Constantinos & Galbraith, Rex F., 1995. "A parametric model for heterogeneity in paired poisson counts," DES - Working Papers. Statistics and Econometrics. WS 10348, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Marron, J S, 1988. "Automatic Smoothing Parameter Selection: A Survey," Empirical Economics, Springer, vol. 13(3/4), pages 187-208.
    3. B. W. Silverman, 1982. "Kernel Density Estimation Using the Fast Fourier Transform," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(1), pages 93-99, March.
    4. Laird, Nan M. & Louis, Thomas A., 1991. "Smoothing the non-parametric estimate of a prior distribution by roughening : A computational study," Computational Statistics & Data Analysis, Elsevier, vol. 12(1), pages 27-37, August.
    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. Berwin A. TURLACH, "undated". "Bandwidth selection in kernel density estimation: a rewiew," Statistic und Oekonometrie 9307, Humboldt Universitaet Berlin.
    2. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    3. Pan, Wei & Louis, Thomas A., 1999. "Two semi-parametric empirical Bayes estimators," Computational Statistics & Data Analysis, Elsevier, vol. 30(2), pages 185-196, April.
    4. Holmström, Lasse, 2000. "The Accuracy and the Computational Complexity of a Multivariate Binned Kernel Density Estimator," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 264-309, February.
    5. A. Quintela del Río & J. Vilar Fernández, 1992. "A local cross-validation algorithm for dependent data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 1(1), pages 123-153, December.
    6. Adriano Z. Zambom & Ronaldo Dias, 2013. "A Review of Kernel Density Estimation with Applications to Econometrics," International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 20-42, April.
    7. Heather L. R. Tierney, 2019. "Forecasting with the Nonparametric Exclusion-from-Core Inflation Persistence Model Using Real-Time Data," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 25(1), pages 39-63, February.
    8. Ignacio N. Lobato, 2000. "A Consistent Test for the Martingale Difference Assumption," Econometric Society World Congress 2000 Contributed Papers 0278, Econometric Society.
    9. del Rio, Alejandro Quintela, 1996. "Comparison of bandwidth selectors in nonparametric regression under dependence," Computational Statistics & Data Analysis, Elsevier, vol. 21(5), pages 563-580, May.
    10. Pinkse, Joris, 1998. "A consistent nonparametric test for serial independence," Journal of Econometrics, Elsevier, vol. 84(2), pages 205-231, June.
    11. Tierney, Heather L.R., 2011. "Real-time data revisions and the PCE measure of inflation," Economic Modelling, Elsevier, vol. 28(4), pages 1763-1773, July.
    12. Tierney, Heather L.R., 2011. "Forecasting and tracking real-time data revisions in inflation persistence," MPRA Paper 34439, University Library of Munich, Germany.
    13. Hardle, W. & Marron, J. S., 1995. "Fast and simple scatterplot smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 20(1), pages 1-17, July.
    14. Rizwan Muhammad & Yaolong Zhao & Fan Liu, 2019. "Spatiotemporal Analysis to Observe Gender Based Check-In Behavior by Using Social Media Big Data: A Case Study of Guangzhou, China," Sustainability, MDPI, vol. 11(10), pages 1-30, May.
    15. Meintanis, S. & Ushakov, N. G., 2004. "Binned goodness-of-fit tests based on the empirical characteristic function," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 305-314, September.
    16. Chung, Yeojin & Lindsay, Bruce G., 2015. "Convergence of the EM algorithm for continuous mixing distributions," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 190-195.
    17. Paddock, Susan M. & Ridgeway, Greg & Lin, Rongheng & Louis, Thomas A., 2006. "Flexible distributions for triple-goal estimates in two-stage hierarchical models," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3243-3262, July.
    18. Scott, David W., 2004. "Multivariate Density Estimation and Visualization," Papers 2004,16, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    19. Tang, Qingguo & Karunamuni, Rohana J., 2016. "Fast and accurate computation for kernel estimators," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 49-62.
    20. Sain, Stephan R., 2002. "Multivariate locally adaptive density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 165-186, April.

    More about this item

    Keywords

    Continuous mixtures;

    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:cte:wsrepe:10437. 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: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    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.