On efficient estimation of densities for sums of squared observations
AbstractDensities of functions of independent and identically distributed random observations can be estimated by using a local U-statistic. Under an appropriate integrability condition, this estimator behaves asymptotically like an empirical estimator. In particular, it converges at the parametric rate. The integrability condition is rather restrictive. It fails for the sum of powers of two observations when the exponent is at least 2. We have shown elsewhere that for the exponent equal to 2 the rate of convergence slows down by a logarithmic factor in the support of the squared observation. Here we show that the estimator is efficient in the sense of Hájek and LeCam. In particular, the convergence rate is optimal.
Download InfoIf 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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 82 (2012)
Issue (Month): 9 ()
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral 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: (Wendy Shamier).
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.