Almost sure uniform convergence rates for M-smoothers with non-monotone score functions
P. K. Bhattacharya and
Peng-liang Zhao
Statistics & Probability Letters, 1993, vol. 16, issue 3, 189-196
Abstract:
Almost sure uniform convergence rates for M-smoothers have been obtained by Härdle, Janssen and Serfling (1988) in the case of bounded, continuous and monotone score functions. In this paper, we show that if there is an initial estimator whose error is a.s. uniformly bounded, then the same rate result holds without the boundedness assumption on the score function [psi](y, t) and with the assumptions of continuity and monotonicity in t replaced by a.s. continuity at each t and a.s. piecewise monotonicity. Since such initial estimators are easy to construct in most situations, this considerably enlarges the scope of the rate result.
Keywords: M-smoothers; strong; uniform; consistency; rate; piecewise; monotone; score; function (search for similar items in EconPapers)
Date: 1993
References: Add references at CitEc
Citations:
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0167-7152(93)90142-6
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:16:y:1993:i:3:p:189-196
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 ().