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高通量筛查中假阳性数量的有效估计AI 解读

This paper develops tail estimation methods to handle false positives in multiple testing problems where testing is done at extreme significance levels and with low degrees of freedom, and where the true null distribution may differ from the theoretical one. We show that the number of false positives, conditional on the total number of positives, has an approximately binomial distribution, and we find estimators of the distribution parameter. We also develop methods for…

簇泛函经验过程的极限定理AI 解读

Let (Xn,i)1≤i≤n,n∈ℕ be a triangular array of row-wise stationary ℝd-valued random variables. We use a “blocks method” to define clusters of extreme values: the rows of (Xn,i) are divided into mn blocks (Yn,j), and if a block contains at least one extreme value, the block is considered to contain a cluster. The cluster starts at the first extreme value in the block and ends at the last one. The main results are uniform central limit theorems for empirical processes $Z_{n}(f):=\frac{1}{\sqrt{nv_{n}}}\sum_{j=1}^{m_{n}}(f(Y_{n,j})-Ef(Y_{n,j}))$…

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