IDEAS home Printed from
   My bibliography  Save this article

Minimum quadratic distance density estimation using nonparametric mixtures


  • Chee, Chew-Seng
  • Wang, Yong


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

    Download full text from publisher

    File URL:
    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

    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. Cao, Ricardo & Cuevas, Antonio & Fraiman, Ricardo, 1995. "Minimum distance density-based estimation," Computational Statistics & Data Analysis, Elsevier, vol. 20(6), pages 611-631, December.
    3. 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.
    4. 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.
    5. 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.
    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.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Denys Pommeret, 2016. "Comparing Two Mixing Densities in Nonparametric Mixture Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 133-153, February.
    2. Chew-Seng Chee, 2016. "Modelling of count data using nonparametric mixtures," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 239-257, July.
    3. 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.


    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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.