Title: Bahadur representation and its applications for local polynomial estimates in nonparametric M -regression
Abstract: In this paper we establish a Bahadur representation for the (kernel weighted) local polynomial estimates in nonparametric M -regression. Both strong Bahadur order O (( nh /log log n ) −3/4 ) and weak Bahadur order O (( nh −3/4 ) are obtained under mild assumptions. As applications, the asymptotic normality and the law of the iterated logarithm are derived. The setting adopted in this paper is very general and our results can be applied to a variety of convex and nonconvex robust regressions as well as likelihood-type regressions. Similar results have been obtained for the local constant fit.
Publication Year: 2003
Publication Date: 2003-01-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 19
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot