摘要
经典的最大均方差异统计量MMD_(b)(F,X,Y)和MMD_(u)^(2)(F,X,Y)基于等量假设(即m=n)来检验两组样本X={x1,x2,……,x_(m)}和Y={y1,y2,……,y_(n)}是否来自不同的分布.本文对样本等量假设进行了放松,推广了经典的最大均方差异统计量界,推导出当m≠n时统计量MMD_(b)(F,X,Y)和MMD_(u)^(2)(F,X,Y)的一般界.结果表明经典的最大均方差异统计量界是本文推导的最大均方差异统计量一般界的特例.
The classical maximum mean discrepancy statistics,i.e.,MMD_(b)(F,X,Y)and MMD_(u)^(2)(F,X,Y),to test whether two samples X={x1,x2,……,x_(m)}xmg and Y={y1,y2,……,y_(n)}yng are drawn from the different distributions p and q.MMDb and MMD2 u are two very useful and effective statistics of which the bounds are derived based on the assumption of m=n.This paper relaxes this assumption and provides the general bounds for these two statistics statistics MMD_(b)and MMD_(u)^(2).The derived results show that the traditional bounds derived in previous study are the special cases of our general bounds.
作者
何玉林
黄德发
戴德鑫
黄哲学
HE Yulin;HUANG Defa;DAI Dexin;HUANG Zhexue(College of Computer Science&Software Engineering,Shenzhen University,Shenzhen 518060,China)
出处
《应用数学》
CSCD
北大核心
2021年第2期284-288,共5页
Mathematica Applicata
基金
Supported by the National Natural Science Foundation of China(61972261)
the Major Statistic Project of National Bureau of Statistics(2020ZX14)
the National Training Program of Innovation and Entrepreneurship for Undergraduates(S202010590028)
the Scientific Research Foundation of Shenzhen University for Newly-introduced Teachers(2018060)。
