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基于极小极大缺损的高维假设最优自适应检验AI 解读

The detection boundary is a tool for power evaluation of a high dimensional test, which provides a binary phase transition of power in terms of signal density and strength. However, it cannot separate the L2 and higher criticism (HC) tests under dense signals, and the L∞ and HC tests under highly sparse signals as they share the same detection boundary. This paper proposes minimax relative deficiency and minimax absolute deficiency as sharper measures for power evaluation…

用于高斯近似的自归一化 Cramér 型中等偏差定理AI 解读

Berry–Esseen type bounds for Gaussian approximation of standardized sums have been extensively studied under exponential type moment conditions. In this paper, a Cramér type moderate deviation theorem is established for self-normalized Gaussian approximation under finite moment conditions. More specifically, let X1,X2,…,Xn be i.i.d. Rp-valued random vectors with zero means. Let Sn,j=∑ i=1nXij and Vn,j2=∑i=1nXij2. We show that if the correlation matrix of X1 is Ip and the…