Abstract
Bootstrap for nonparametric regression has been around for more than 30 years. Nevertheless, most results are based on assuming an additive regression model with respect to independent and identical (i.i.d.) errors. An exception is the Local Bootstrap of Shi [23] for which, however, no bootstrap consistency results are available. We attempt to remedy this here while at the same time showing bootstrap consistency for a more general class of methods that fall under the heading of Model-free Bootstrap of Politis [18].
Highlights
Consider regression data {(Yi, Xi)}, i = 1, . . . , n which are independent and identical (i.i.d.) pairs
In this paper we will provide the first theoretical results on Model-free bootstrap consistency, and we will further compare to the Local bootstrap by simulation
We reveal a close relationship between the two methods under specified assumptions, i.e., the Local bootstrap is essentially a special case of the Model-free bootstrap
Summary
Before describing the notion of Model-free Bootstrap it is important to note that Efron’s [3] well-known method of resampling pairs has a chance does not work appropriately in nonparametric regression. In this paper we will provide the first theoretical results on Model-free bootstrap consistency, and we will further compare to the Local bootstrap by simulation. We reveal a close relationship between the two methods under specified assumptions, i.e., the Local bootstrap is essentially a special case of the Model-free bootstrap Both the Local bootstrap and the Model-free bootstrap can be implemented using any form of nonparametric regression estimators, to fix ideas in this paper we focus on the Nadaraya-Watson (N-W) kernel estimator [11]: mn,h(x) =. The following is a brief introduction to the spirit of Local bootstrap and Model-free method in regression problem; more details can be found in sections 3 and 4. Proofs of most lemmas and theorems can be found in the Appendix
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
