IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Nonparametric estimation of multivariate elliptic densities via finite mixture sieves

  • Heather Battey
  • Oliver Linton

    ()

    (Institute for Fiscal Studies and Cambridge University)

This paper considers the class of p-dimensional elliptic distributions (p ≥ 1) satisfying the consistency property (Kano, 1994) and within this general framework presents a two-stage semiparametric estimator for the Lebesgue density based on Gaussian mixture sieves. Under the online Exponentiated Gradient (EG) algorithm of Helmbold et al. (1997) and without restricting the mixing measure to have compact support, the estimator produces estimates converging uniformly in probability to the true elliptic density at a rate that is independent of the dimension of the problem, hence circumventing the familiar curse of dimensionality inherent to many semiparametric estimators. The rate performance of our estimator depends on the tail behaviour of the underlying mixing density (and hence that of the data) rather than smoothness properties. In fact, our method achieves a rate of at least Op(n-1/4), provided only some positive moment exists. When further moments exist, the rate improves reaching Op(n-3/8) as the tails of the true density converge to those of a normal. Unlike the elliptic density estimator of Liebscher (2005), our sieve estimator always yields an estimate that is valid density, and is also attractive from a practical perspective as it accepts data as a stream, thus significantly reducing computational and storage requirements. Monte Carlo experimentation indicates encouraging finite sample performance over a range of elliptic densities. The estimator is also implemented in a binary classification task using the well-known Wisconsin breast cancer dataset.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.cemmap.ac.uk/wps/cwp151313.pdf
Download Restriction: no

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP15/13.

as
in new window

Length:
Date of creation: Apr 2013
Date of revision:
Handle: RePEc:ifs:cemmap:15/13
Contact details of provider: Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
Phone: (+44) 020 7291 4800
Fax: (+44) 020 7323 4780
Web page: http://cemmap.ifs.org.uk
Email:


More information through EDIRC

Order Information: Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
Email:


References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Sain, Stephan R., 2002. "Multivariate locally adaptive density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 39(2), pages 165-186, April.
  2. 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.
  3. Patrick Marsh, 2007. "Constructing Optimal tests on a Lagged dependent variable," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(5), pages 723-743, 09.
  4. Liebscher, Eckhard, 2005. "A semiparametric density estimator based on elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 205-225, January.
  5. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
  6. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
  7. Berk, Jonathan B., 1997. "Necessary Conditions for the CAPM," Journal of Economic Theory, Elsevier, vol. 73(1), pages 245-257, March.
  8. Abdul-Hamid, Husein & Nolan, John P., 1998. "Multivariate Stable Densities as Functions of One Dimensional Projections," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 80-89, October.
  9. Hajo Holzmann & Axel Munk & Tilmann Gneiting, 2006. "Identifiability of Finite Mixtures of Elliptical Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 753-763.
  10. Owen, Joel & Rabinovitch, Ramon, 1983. " On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-52, June.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:ifs:cemmap:15/13. 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: (Stephanie Seavers)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.