Asymptotic Normality of Statistics Based on the Convex Minorants of Empirical Distribution Functions
Asymptotic Normality of Statistics Based on the Convex Minorants of Empirical Distribution Functions
复制标题
基于经验分布函数凸次式的统计渐进正态性
DOI：
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发表时间：
1983
期刊：
影响因子：
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通讯作者：
R. Pyke
中科院分区：
文献类型：
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作者：
P. Groeneboom;R. Pyke
设F_i为均匀经验分布函数。写Fn为F的（最小）凹优数，并让An表示相应的密度。它表明，nfl（？fn（t）1）2 dt在以log n为中心并以（3 log n）1I2归一化时是渐近标准正态的。在2样本情况下得到类似的结果，其中fn由Fm = Fm HN 1的凸次项的斜率代替。
Let F,, be the Uniform empirical distribution function. Write Fn for the (least) concave majorant of F, and let An denote the corresponding density. It is shown that n fl (?fn(t) 1)2 dt is asymptotically standard normal when centered at log n and normalized by (3 log n)1I2. A similar result is obtained in the 2-sample case in which fn is replaced by the slope of the convex minorant of Fm = Fm HN1.