Advanced Search
MyIDEAS: Login

Generalized single-index models: The EFM approach

Contents:

Author Info

  • Xia Cui
  • Wolfgang Karl Härdle
  • Lixing Zhu

Abstract

Generalized single-index models are natural extensions of linear models and circumvent the so-called curse of dimensionality. They are becoming increasingly popular in many scientific fields including biostatistics, medicine, economics and finan- cial econometrics. Estimating and testing the model index coefficients beta is one of the most important objectives in the statistical analysis. However, the commonly used assumption on the index coefficients, beta = 1, represents a non-regular problem: the true index is on the boundary of the unit ball. In this paper we introduce the EFM ap- proach, a method of estimating functions, to study the generalized single-index model. The procedure is to first relax the equality constraint to one with (d - 1) components of beta lying in an open unit ball, and then to construct the associated (d - 1) estimating functions by projecting the score function to the linear space spanned by the residuals with the unknown link being estimated by kernel estimating functions. The root-n consistency and asymptotic normality for the estimator obtained from solving the re- sulting estimating equations is achieved, and a Wilk's type theorem for testing the index is demonstrated. A noticeable result we obtain is that our estimator for beta has smaller or equal limiting variance than the estimator of Carroll et al. (1997). A fixed point iterative scheme for computing this estimator is proposed. This algorithm only involves one-dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Numerical studies based on simulation and on applications suggest that this new estimating system is quite powerful and easy to implement.

Download Info

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://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2009-050.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2009-050.

as in new window
Length: 39 pages
Date of creation: Oct 2009
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2009-050

Contact details of provider:
Postal: Spandauer Str. 1,10178 Berlin
Phone: +49-30-2093-5708
Fax: +49-30-2093-5617
Email:
Web page: http://sfb649.wiwi.hu-berlin.de
More information through EDIRC

Related research

Keywords: Generalized single-index model; index coefficients; estimating equations; asymptotic properties; iteration;

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

No references listed on IDEAS
You can help add them by filling out this form.

Citations

Lists

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

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:hum:wpaper:sfb649dp2009-050. 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: (RDC-Team).

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.