Abstract
We present some key probability inequalities and convergence results for multisample, or ‘generalized’ U-statistics. The reverse martingale structure of generalized U-statistic is exploited to obtain a useful Kolmogorov-type inequality. In addition, a bound is obtained for the rate of convergence in the strong law of large numbers for generalized U-statistics, expanding the one-sample result of Grams and Serfling (1973). Also, using a forward martingale representation, an invariance principle for generalized U-statistics is established.
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.
