The distribution and quantiles of functionals of weighted empirical distributions when observations have different distributions
This paper extends Edgeworth-Cornish-Fisher expansions for the distribution and quantiles of nonparametric estimates in two ways. Firstly, it allows observations to have different distributions. Secondly, it allows the observations to be weighted in a predetermined way. The use of weighted estimates has a long history, including applications to regression, rank statistics and Bayes theory. However, asymptotic results have generally been only first order (the CLT and weak convergence). We give third order asymptotics for the distribution and percentiles of any smooth functional of a weighted empirical distribution, thus allowing a considerable increase in accuracy over earlier CLT results. Consider independent non-identically distributed (non-iid) observations X1n,...,Xnn in Rs. Let be their weighted empirical distribution with weights w1n,...,wnn. We obtain cumulant expansions and hence Edgeworth-Cornish-Fisher expansions for for any smooth functional T([dot operator]) by extending the concepts of von Mises derivatives to signed measures of total measure 1. As an example we give the cumulant coefficients needed for Edgeworth-Cornish-Fisher expansions to O(n-3/2) for the sample coefficient of variation when observations are non-iid.
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): 80 (2010)
Issue (Month): 13-14 (July)
|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.:
- C. Withers, 1988. "Nonparametric confidence intervals for functions of several distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 727-746, December.