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超越高阶批判：对稀少弱信号备择更敏感的检验AI 解读

Higher criticism (HC) is a popular method for large-scale inference problems based on identifying unusually high proportions of small $p$-values. It has been shown to enjoy a lower-order optimality property in a simple normal location mixture model which is shared by the ‘tailor-made’ parametric generalised likelihood ratio test (GLRT) for the same model; however, HC has also been shown to perform well outside this ‘narrow’ model. We develop a higher-order framework for…

多维对数凹密度的最大似然估计AI 解读

Summary Let X1,…,Xn be independent and identically distributed random vectors with a (Lebesgue) density f. We first prove that, with probability 1, there is a unique log-concave maximum likelihood estimator f^n of f. The use of this estimator is attractive because, unlike kernel density estimation, the method is fully automatic, with no smoothing parameters to choose. Although the existence proof is non-constructive, we can reformulate the issue of computing f^n in terms of…