Abstract
In the Gaussian white noise model, we study the estimation of an unknown multidimensional function f in the uniform norm by using kernel methods. We determine the sets of functions that are well estimated at the rates (log n/n) β/(2β+d) and n −β/(2β+d) by kernel estimators. These sets are called maxisets. Then, we characterize the maxisets associated to kernel estimators and to the Lepski procedure for the rate of convergence (log n/n) β/(2β+d) in terms of Besov and Hölder spaces of regularity β. Using maxiset results, optimal choices for the bandwidth parameter of kernel rules are derived. Performances of these rules are studied from the numerical point of view.
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.
