Abstract
In this paper we use a central limit theorem for entropy due to Ibragimov to obtain limit theorems for linear normalizations of the log minimum distance when observations are sampled from measures belonging to a family of fractal distributions. It is shown that in almost all cases the limit distribution is Gaussian with parameters determined in part by the Hausdorff dimension associated with the underlying measure. Exceptions to this rule include absolutely continuous measures which obey the classical extreme value limit laws.
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.
