IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v57y2013i1p1-16.html
   My bibliography  Save this article

Minimum quadratic distance density estimation using nonparametric mixtures

Author

Listed:
  • Chee, Chew-Seng
  • Wang, Yong

Abstract

Quadratic loss is predominantly used in the literature as the performance measure for nonparametric density estimation, while nonparametric mixture models have been studied and estimated almost exclusively via the maximum likelihood approach. In this paper, we relate both for estimating a nonparametric density function. Specifically, we consider nonparametric estimation of a mixing distribution by minimizing the quadratic distance between the empirical and the mixture distribution, both being smoothed by kernel functions, a technique known as double smoothing. Experimental studies show that the new mixture-based density estimators outperform the popular kernel-based density estimators in terms of mean integrated squared error for practically all the distributions that we studied, thanks to the substantial bias reduction provided by nonparametric mixture models and double smoothing.

Suggested Citation

  • Chee, Chew-Seng & Wang, Yong, 2013. "Minimum quadratic distance density estimation using nonparametric mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 1-16.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:1-16
    DOI: 10.1016/j.csda.2012.06.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312002447
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.06.004?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. Seo, Byungtae & Lindsay, Bruce G., 2010. "A computational strategy for doubly smoothed MLE exemplified in the normal mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1930-1941, August.
    2. Yong Wang, 2007. "On fast computation of the non‐parametric maximum likelihood estimate of a mixing distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 185-198, April.
    3. Ayanendranath Basu & Bruce Lindsay, 1994. "Minimum disparity estimation for continuous models: Efficiency, distributions and robustness," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 683-705, December.
    4. Cao, Ricardo & Cuevas, Antonio & Fraiman, Ricardo, 1995. "Minimum distance density-based estimation," Computational Statistics & Data Analysis, Elsevier, vol. 20(6), pages 611-631, December.
    5. Jones, M.C. & Henderson, D.A., 2009. "Maximum likelihood kernel density estimation: On the potential of convolution sieves," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3726-3733, August.
    6. repec:dau:papers:123456789/4650 is not listed on IDEAS
    7. Fadoua Balabdaoui & Jon A. Wellner, 2010. "Estimation of a k‐monotone density: characterizations, consistency and minimax lower bounds," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 45-70, February.
    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. Chee, Chew-Seng & Wang, Yong, 2014. "Least squares estimation of a k-monotone density function," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 209-216.

    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. Sangyeol Lee & Junmo Song, 2013. "Minimum density power divergence estimator for diffusion processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 213-236, April.
    2. Balabdaoui, Fadoua & Kulagina, Yulia, 2020. "Completely monotone distributions: Mixing, approximation and estimation of number of species," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    3. Seo, Byungtae, 2017. "The doubly smoothed maximum likelihood estimation for location-shifted semiparametric mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 27-39.
    4. Basu, Ayanendranath & Lindsay, Bruce G., 2004. "The iteratively reweighted estimating equation in minimum distance problems," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 105-124, March.
    5. Chee, Chew-Seng & Wang, Yong, 2016. "Nonparametric estimation of species richness using discrete k-monotone distributions," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 107-118.
    6. Kang, Jiwon & Lee, Sangyeol, 2014. "Minimum density power divergence estimator for Poisson autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 44-56.
    7. Mercedes Fernandez Sau & Daniela Rodriguez, 2018. "Minimum distance method for directional data and outlier detection," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 587-603, September.
    8. Chee, Chew-Seng & Wang, Yong, 2014. "Least squares estimation of a k-monotone density function," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 209-216.
    9. Arun Kumar Kuchibhotla & Somabha Mukherjee & Ayanendranath Basu, 2019. "Statistical inference based on bridge divergences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 627-656, June.
    10. Madeleine Cule & Richard Samworth & Michael Stewart, 2010. "Maximum likelihood estimation of a multi‐dimensional log‐concave density," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 545-607, November.
    11. Roberto Mari & Roberto Rocci & Stefano Antonio Gattone, 2020. "Scale-constrained approaches for maximum likelihood estimation and model selection of clusterwise linear regression models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 49-78, March.
    12. Gayen, Atin & Kumar, M. Ashok, 2021. "Projection theorems and estimating equations for power-law models," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    13. Seo, Byungtae & Kim, Daeyoung, 2012. "Root selection in normal mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2454-2470.
    14. Giovanni Saraceno & Claudio Agostinelli & Luca Greco, 2021. "Robust estimation for multivariate wrapped models," METRON, Springer;Sapienza Università di Roma, vol. 79(2), pages 225-240, August.
    15. Luca Greco & Giovanni Saraceno & Claudio Agostinelli, 2021. "Robust Fitting of a Wrapped Normal Model to Multivariate Circular Data and Outlier Detection," Stats, MDPI, vol. 4(2), pages 1-18, June.
    16. Sangyeol Lee & Okyoung Na, 2005. "Test for parameter change based on the estimator minimizing density-based divergence measures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 553-573, September.
    17. Giguelay, J. & Huet, S., 2018. "Testing k-monotonicity of a discrete distribution. Application to the estimation of the number of classes in a population," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 96-115.
    18. A. Philip Dawid & Monica Musio & Laura Ventura, 2016. "Minimum Scoring Rule Inference," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 123-138, March.
    19. M. Ryan Haley & Todd B. Walker, 2010. "Alternative tilts for nonparametric option pricing," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(10), pages 983-1006, October.
    20. 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.

    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:57:y:2013:i:1:p:1-16. 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.