Random Deletion Does Not Affect Asymptotic Normality or Quadratic Negligibility
Suppose a number of points are deleted from a sample of random vectors in d. The number of deleted points may depend on the sample sizen, and on any other sample information, provided only that it is bounded in probability asn-->[infinity]. In particular, "extremes" of the sample, however defined, may be deleted. We show that this operation has no effect on the asymptotic normality of the sample sum, in the sense that the sum of the deleted sample is asymptotically normal, after norming and centering, if and only if the sample sum itself is asymptotically normal with the same norming and centering as the deleted sum. That is, the sample must be drawn from a distribution in the domain of attraction of the multivariate normal distribution. The domain of attraction concept we employ uses general operator norming and centering, as developed by Hahn and Klass. We also show that random deletion has no effect on the "quadratic negligibility" of the sample. These are conditions that are important in the robust analysis of multivariate data and in regression problems, for example.
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.
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.
Volume (Year): 63 (1997)
Issue (Month): 1 (October)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
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.:
- Vu, H. T. V. & Maller, R. A. & Klass, M. J., 1996. "On the Studentisation of Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 57(1), pages 142-155, April.
- Maller, R. A., 1993. "Quadratic Negligibility and the Asymptotic Normality of Operator Normed Sums," Journal of Multivariate Analysis, Elsevier, vol. 44(2), pages 191-219, February.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:63:y:1997:i:1:p:136-179. 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: (Shamier, Wendy)
If references are entirely missing, you can add them using this form.