CONVERGENCE OF SCALED RANDOM SAMPLES IN RD
成果类型：
Article
署名作者：
KINOSHITA, K; RESNICK, SI
署名单位：
Cornell University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176990227
发表日期：
1991
页码：
1640-1663
关键词：
摘要：
Let {X(j), 1 less-than-or-equal-to j less-than-or-equal-to n} be a sequence of iid random vectors in R(d) and S(n) = {X(j)/b(n), 1 less-than-or-equal-to j less-than-or-equal-to n}. When do there exist scaling constants b(n) --> infinity such that S(n) converges to some compact set S in R(d) almost surely (in probability)? We show that a limit set S is star-shaped (i.e., x is-an-element-of S implies tx is-an-element-of S, for 0 less-than-or-equal-to t less-than-or-equal-to 1) so that after a polar coordinate transformation the limit set is the hypograph of an upper semicontinuous function. We specify necessary and sufficient conditions for convergence to a particular limit set. Some examples are also given.