Related papers: Cauchy combination test: a powerful test with anal…
We are concerned with testing replicability hypotheses for many endpoints simultaneously. This constitutes a multiple test problem with composite null hypotheses. Traditional $p$-values, which are computed under least favourable parameter…
The classical theory for the meta-analysis of $p$-values is based on the assumption that if the overall null hypothesis is true, then all $p$-values used in a chosen combined test statistic are genuine, i.e., are observations from…
Various methods of combining individual p-values into one p-value are widely used in many areas of statistical applications. We say that a combining method is valid for arbitrary dependence (VAD) if it does not require any assumption on the…
Combining p-values from independent statistical tests is a popular approach to meta-analysis, particularly when the data underlying the tests are either no longer available or are difficult to combine. A diverse range of p-value combination…
We develop a unified $L$-statistic testing framework for high-dimensional regression coefficients that adapts to unknown sparsity. The proposed statistics rank coordinate-wise evidence measures and aggregate the top $k$ signals, bridging…
This paper proposes general methods for the problem of multiple testing of a single hypothesis, with a standard goal of combining a number of p-values without making any assumptions about their dependence structure. An old result by…
Categorical variables are of uttermost importance in biomedical research. When two of them are considered, it is often the case that one wants to test whether or not they are statistically dependent. We show weaknesses of classical methods…
The test of independence is a crucial component of modern data analysis. However, traditional methods often struggle with the complex dependency structures found in high-dimensional data. To overcome this challenge, we introduce a novel…
Testing mutual independence among multiple random variables is a fundamental problem in statistics, with wide applications in genomics, finance, and neuroscience. In this paper, we propose a new class of tests for high-dimensional mutual…
Permutation tests are a distribution free way of performing hypothesis tests. These tests rely on the condition that the observed data are exchangeable among the groups being tested under the null hypothesis. This assumption is easily…
Selective inference is a subfield of statistics that enables valid inference after selection of a data-dependent question. In this paper, we introduce selectively dominant p-values, a class of p-values that allow practitioners to easily…
The Cauchy combination test (CCT) is widely used because it gives a closed-form combined $p$-value and is known to be asymptotically valid as the nominal level $\alpha\downarrow0$ under broad dependence structures. We study a different…
The practice of pooling several individual test statistics to form aggregate tests is common in many statistical application where individual tests may be underpowered. While selection by aggregate tests can serve to increase power, the…
The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…
We theoretically analyze the problem of testing for $p$-hacking based on distributions of $p$-values across multiple studies. We provide general results for when such distributions have testable restrictions (are non-increasing) under the…
We introduce a new characterization of the Cauchy distribution and propose a class of goodness-of-fit tests to the Cauchy family. The limit distribution is derived in a Hilbert space framework under the null hypothesis and under fixed…
The present paper gives a statistical adventure towards exploring the average case complexity behavior of computer algorithms. Rather than following the traditional count based analytical (pen and paper) approach, we instead talk in terms…
We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
In the machine learning era, sparsity continues to attract significant interest due to the benefits it provides to learning models. Algorithms aiming to optimise the \(\ell_0\)- and \(\ell_1\)-norm are the common choices to achieve…