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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…
We consider finite-sample inference for a single regression coefficient in the fixed-design linear model $Y = Z\beta + bX + \varepsilon$, where $\varepsilon\in\mathbb{R}^n$ may exhibit complex dependence or heterogeneity. We develop a group…
Permutation tests are widely used in statistics, providing a finite-sample guarantee on the type I error rate whenever the distribution of the samples under the null hypothesis is invariant to some rearrangement. Despite its increasing…
Generalizations to the permutation test are introduced to allow for situations in which the null model is not exchangeable. It is shown that the generalized permutation tests are exact, and a partial converse: that any test function that is…
Test statistics are often strongly dependent in large-scale multiple testing applications. Most corrections for multiplicity are unduly conservative for correlated test statistics, resulting in a loss of power to detect true positives. We…
Monte Carlo permutation tests are a cornerstone of valid, model-free statistical inference. A widely held practical intuition is that increasing the number of sampled permutations improves test performance, in particular that statistical…
The stochastic block model is widely used for detecting community structures in network data. However, the research interest of much literature focuses on the study of one sample of stochastic block models. How to detect the difference of…
Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper proposes permutation tests…
This paper studies one-sided hypothesis testing under random sampling without replacement. That is, when $n+1$ binary random variables $X_1,\ldots, X_{n+1}$ are subject to a permutation invariant distribution and $n$ binary random variables…
Given independent samples from P and Q, two-sample permutation tests allow one to construct exact level tests when the null hypothesis is P=Q. On the other hand, when comparing or testing particular parameters $\theta$ of P and Q, such as…
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…
Reliable estimation of feature contributions in machine learning models is essential for trust, transparency and regulatory compliance, especially when models are proprietary or otherwise operate as black boxes. While permutation-based…
Permutation tests are a popular choice for distinguishing distributions and testing independence, due to their exact, finite-sample control of false positives and their minimax optimality when paired with U-statistics. However, standard…
Many testing problems are readily amenable to randomised tests such as those employing data splitting. However despite their usefulness in principle, randomised tests have obvious drawbacks. Firstly, two analyses of the same dataset may…
The stochastic block model is a popular tool for detecting community structures in network data. Detecting the difference between two community structures is an important issue for stochastic block models. However, the two-sample test has…
Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates.…
Testing differences in mean vectors is a fundamental task in the analysis of high-dimensional compositional data. Existing methods may suffer from low power if the underlying signal pattern is in a situation that does not favor the deployed…
In many applied sciences a popular analysis strategy for high-dimensional data is to fit many multivariate generalized linear models in parallel. This paper presents a novel approach to address the resulting multiple testing problem by…
Permutation-based partial-correlation tests guarantee finite-sample Type I error control under any fixed design and exchangeable noise, yet their power can collapse when the permutation-augmented design aligns too closely with the covariate…
In the big data era, the need to reevaluate traditional statistical methods is paramount due to the challenges posed by vast datasets. While larger samples theoretically enhance accuracy and hypothesis testing power without increasing false…