A Theorem on Uniform Convergence of Stochastic Functions with Applications

Ke-Hai Yuan

Journal of Multivariate Analysis, 1997, vol. 62, issue 1, 100-109

Abstract: In a variety of statistical problems one needs to manipulate a sequence of stochastic functions involving some unknown parameters. The asymptotic behavior of the estimated parameters often depends on the asymptotic properties of such functions. Especially, the consistency of the estimated parameters follows from the uniform convergence of the sequence of stochastic functions. A theorem on uniform convergence of a sequence of vector valued random functions is presented. The forms of these functions are very general and the assumptions are rather natural. If the sequence of random functions is generated by a sequence of random vectors, these random vectors are only required to be independently distributed and can be of different dimensions. As applications, we consider the consistency of the estimated regression parameters in logistic regression and in M-estimation in a linear model.

Keywords: uniform; convergence; strong; consistency; logistic; regression; M-estimation (search for similar items in EconPapers)
Date: 1997
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047-259X(97)91674-2
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:jmvana:v:62:y:1997:i:1:p:100-109

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

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().