Related papers: Higher criticism: $p$-values and criticism
Large-scale multiple testing problems require the simultaneous assessment of many p-values. This paper compares several methods to assess the evidence in multiple binomial counts of p-values: the maximum of the binomial counts after…
We consider the problem of detecting a sparse mixture as studied by Ingster (1997) and Donoho and Jin (2004). We consider a wide array of base distributions. In particular, we study the situation when the base distribution has polynomial…
Higher criticism, or second-level significance testing, is a multiple-comparisons concept mentioned in passing by Tukey. It concerns a situation where there are many independent tests of significance and one is interested in rejecting the…
Donoho and Kipnis (2022) showed that the the higher criticism (HC) test statistic has a non-Gaussian phase transition but remarked that it is probably not optimal, in the detection of sparse differences between two large frequency tables…
We consider two alternative tests to the Higher Criticism test of Donoho and Jin [Ann. Statist. 32 (2004) 962-994] for high-dimensional means under the sparsity of the nonzero means for sub-Gaussian distributed data with unknown column-wise…
Continuous goodness-of-fit testing is a classical problem in statistics. Despite having low power for detecting deviations at the tail of a distribution, the most popular test is based on the Kolmogorov-Smirnov statistic. While similar…
It is quite common in modern research, for a researcher to test many hypotheses. The statistical (frequentist) hypothesis testing framework, does not scale with the number of hypotheses in the sense that naively performing many hypothesis…
P-values are widely used in both the social and natural sciences to quantify the statistical significance of observed results. The recent surge of big data research has made the p-value an even more popular tool to test the significance of…
A unified family of goodness-of-fit tests based on $\phi$-divergences is introduced and studied. The new family of test statistics $S_n(s)$ includes both the supremum version of the Anderson--Darling statistic and the test statistic of Berk…
We describe, in the detection of multi-sample aligned sparse signals, the critical boundary separating detectable from nondetectable signals, and construct tests that achieve optimal detectability: penalized versions of the Berk-Jones and…
We propose a new method of gravitational wave detection using a modified form of higher criticism, a statistical technique introduced by Donoho & Jin (2004). Higher criticism is designed to detect a group of sparse, weak sources, none of…
A fundamental problem in high-dimensional testing is that of global null testing: testing whether the null holds simultaneously in all of $n$ hypotheses. The max test, which uses the smallest of the $n$ marginal p-values as its test…
We consider the problem of detecting a sparse Poisson mixture. Our results parallel those for the detection of a sparse normal mixture, pioneered by Ingster (1997) and Donoho and Jin (2004), when the Poisson means are larger than…
In big data analysis for detecting rare and weak signals among $n$ features, some grouping-test methods such as Higher Criticism test (HC), Berk-Jones test (B-J), and $\phi$-divergence test share the similar asymptotical optimality when $n…
We propose a method for comparing survival data based on the higher criticism of p-values obtained from multiple exact hypergeometric tests. The method accommodates non-informative right-censorship and is sensitive to hazard differences in…
Higher criticism is a method for detecting signals that are both sparse and weak. Although first proposed in cases where the noise variables are independent, higher criticism also has reasonable performance in settings where those variables…
In a bivariate setting, we consider the problem of detecting a sparse contamination or mixture component, where the effect manifests itself as a positive dependence between the variables, which are otherwise independent in the main…
In modern high-throughput data analysis, researchers perform a large number of statistical tests, expecting to find perhaps a small fraction of significant effects against a predominantly null background. Higher Criticism (HC) was…
Higher Criticism is a recently developed statistic for non-Gaussian detection, proposed in Donoho & Jin 2004. We find that Higher Criticism is useful for two purposes. First, Higher Criticism has competitive detection power, and…
In an attempt to provide an answer to the increasing criticism against p-values and to bridge the gap between statistical inference and prediction modelling, we introduce the probability of improved prediction (PIP). In general, the PIP is…