The distribution and quantiles of functionals of weighted empirical distributions when observations have different distributions

Christopher S. Withers and Saralees Nadarajah

Statistics & Probability Letters, 2010, vol. 80, issue 13-14, 1093-1102

Abstract: 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.

Keywords: Edgeworth-Cornish-Fisher; expansions; von; Mises; derivatives; Weighted; empirical; distribution (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(10)00073-8
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:80:y:2010:i:13-14:p:1093-1102

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().