Related papers: Higher criticism for detecting sparse heterogeneou…

We consider the problem of detecting sparse heterogeneous mixtures in a two-sample setting from a nonparametric perspective, where the effect manifests itself as a positive shift. We suggest a two-sample higher criticism test, and show that…

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…

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…

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…

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 study the signal detection problem in high dimensional noise data (possibly) containing rare and weak signals. Log-likelihood ratio (LLR) tests depend on unknown parameters, but they are needed to judge the quality of detection tests…

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…

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…

This paper compares the higher criticism statistic (Donoho and Jin [Ann. Statist. 32 (2004) 962-994]), a modification of the higher criticism statistic also suggested by Donoho and Jin, and two statistics of the Berk-Jones [Z. Wahrsch.…

Consider a multiple hypothesis testing setting involving rare/weak effects: relatively few tests, out of possibly many, deviate from their null hypothesis behavior. Summarizing the significance of each test by a P-value, we construct a…

We consider the problem of detecting sparse heterogeneous mixtures from a nonparametric perspective, and develop distribution-free tests when all effects have the same sign. Specifically, we assume that the null distribution is symmetric…

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 adapt Higher Criticism (HC) to the comparison of two frequency tables which may -- or may not -- exhibit moderate differences between the tables in some unknown, relatively small subset out of a large number of categories. Our analysis…

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…

In the presence of weak overall correlation, it may be useful to investigate if the correlation is significantly and substantially more pronounced over a subpopulation. Two different testing procedures are compared. Both are based on the…

For high dimensional statistical models, researchers have begun to focus on situations which can be described as having relatively few moderately large coefficients. Such situations lead to some very subtle statistical problems. In…

The problem of signal detection using sparse, faint information is closely related to a variety of contemporary statistical problems, including the control of false-discovery rate, and classification using very high-dimensional data. Each…

There is a well-known problem in Null Hypothesis Significance Testing: many statistically significant results fail to replicate in subsequent experiments. We show that this problem arises because standard `point-form null' significance…

Large-scale simultaneous hypothesis testing appears in many areas such as microarray studies, genome-wide association studies, brain imaging, disease mapping and astronomical surveys. A well-known inference method is to control the false…

Higher criticism is a large-scale testing procedure that can attain the optimal detection boundary for sparse and faint signals. However, there has been a lack of knowledge in most existing works about its asymptotic distribution for more…