Strong bounds for multidimensional spacings
Strong bounds for multidimensional spacings
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多维间距的强界限
DOI：
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发表时间：
1983
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影响因子：
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通讯作者：
P. Deheuvels
中科院分区：
文献类型：
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作者：
P. Deheuvels
摘要U1，U2，...，未独立的随机矢量均匀分布在（0，1）d上。在（0,1）D中的d维平方块的一侧的可能值，该块不相交，并且如果不这样做，则无法增加。 n -1（log n+0（log2n））} 1/d几乎可以肯定由于n→∞提出了其他边界，以确保Δn（k）的限制行为为n→∞。
SummaryLet U1, U2,..., Un be independent random vectors uniformly distributed on (0, 1)d. We define the k-th maximal spacing Δn(k) associated to U1, ...,U1 as the k-th maximal possible value of the length of a side of a d-dimensional square block in (0,1) d, which does not intersect the sample, and which cannot be enlarged without doing so. Our main result is that Δn(k)={n−1(Log n+0(Log2n))} 1/d almost surely as n→∞. Other bounds are proposed for the limiting almost sure behavior of Δn(k) as n→∞.