The weighted empirical process of row independent random variables with arbitrary distribution functions

Galen R. Shorack

Statistica Neerlandica, 1979, vol. 33, issue 4, 169-189

Abstract: Abstract The relative compactness and weak convergence of reduced empirical, quantile and weighted empirical processes are demonstrated under mild conditions. For example, the reduced empirical proces of arbitrary independent iv'S is always relatively compact in any ‖/q‖ metric with q square integrable; and weak convergence takes place if and only if the covariance function converges. Van Zuijlen's representation of the general empirical process is a fundamental tool. This paper both unifies and extends the previous treatment of these processes ‐ processes that have application to rank statistics and linear combinations of order statistics. Most proofs are contained in Section 3. A brief introduction to weak convergence is presented in the appendix for readers lacking this background. Applications are indicated in Section 4.

Date: 1979
References: Add references at CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
https://doi.org/10.1111/j.1467-9574.1979.tb00673.x

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:bla:stanee:v:33:y:1979:i:4:p:169-189

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0039-0402

Access Statistics for this article

Statistica Neerlandica is currently edited by Miroslav Ristic, Marijtje van Duijn and Nan van Geloven

More articles in Statistica Neerlandica from Netherlands Society for Statistics and Operations Research
Bibliographic data for series maintained by Wiley Content Delivery ().