Large Deviations of Goodness of Fit Statistics and Linear Combinations of Order Statistics
Large Deviations of Goodness of Fit Statistics and Linear Combinations of Order Statistics
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拟合优度统计的大偏差和阶次统计的线性组合
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发表时间：
1981
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影响因子：
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通讯作者：
G. Shorack
中科院分区：
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作者：
P. Groeneboom;G. Shorack
研究了经验分布函数大偏差的渐近行为。Borovkov(1967)和Hoadley(1967)得到了泛函在DF集上的超范数拓扑中连续的结果。Groeneom，Oosterhoff和Ruymgaart(1979)将其推广到Func-S在更强的‘I-拓扑中。这个结果现在被推广到仅在DF的一个特定有用子集上是[-连续的泛函。我们考虑了Anderson-Darling统计量和顺序统计量的线性组合的应用。我们首先修正了Abrahamson(1967)的工作；由此发现了关键权函数W(T)=-logt(L-t)的作用。然后利用它来达到上述目的，并在拟合测试中将其视为一个权重函数。
Asymptotic behavior of large deviations of empirical distribution functions (df's) is considered. Borovkov (1967) and Hoadley (1967) obtained results for functionals continuous in the sup norm topology on the set of df's. Groeneboom, Oosterhoff, and Ruymgaart (1979) extended this to func-s in a stronger 'I-topology This result is now extended to functionals that are "[-continuous only on a particular useful subset of df's. Applications to the Anderson-Darling statistic and linear combinations of order statistics are considered. We begin by correcting the work of Abrahamson (1967); from this the role of the key weight function W(t) =-log t(l-t) is discovered. It is then exploited to the end indicated above, and it is considered as a weight function in tests of fit.