Abstract
Given a random vector X valued in ℝ d with density f and an arbitrary probability number p∈(0; 1), we consider the estimation of the upper level set<texlscub>f≥t (p)</texlscub>of f corresponding to probability content p, that is, such that the probability that X belongs to<texlscub>f≥t (p)</texlscub>is equal to p. Based on an i.i.d. random sample X 1, …, X n drawn from f, we define the plug-in level set estimate , where is a random threshold depending on the sample and [fcirc] n is a nonparametric kernel density estimate based on the same sample. We establish the exact convergence rate of the Lebesgue measure of the symmetric difference between the estimated and actual level sets.
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.
