Related papers: Minimax optimality of permutation tests
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…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…
Based on two independent samples X_1,...,X_m and X_{m+1},...,X_n drawn from multivariate distributions with unknown Lebesgue densities p and q respectively, we propose an exact multiple test in order to identify simultaneously regions of…
When permutation methods are used in practice, often a limited number of random permutations are used to decrease the computational burden. However, most theoretical literature assumes that the whole permutation group is used, and methods…
Given observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing…
There has been much interest in the nonparametric testing of conditional independence in the econometric and statistical literature, but the simplest and potentially most useful method, based on the sample partial correlation, seems to have…
Econometric applications with multi-way clustering often feature a small number of effective clusters or heavy-tailed data, making standard cluster-robust and bootstrap inference unreliable in finite samples. In this paper, we develop a…
We propose a new powerful family of tests of univariate normality. These tests are based on an initial value problem in the space of characteristic functions originating from the fixed point property of the normal distribution in the zero…
We propose using a permutation test to detect discontinuities in an underlying economic model at a known cutoff point. Relative to the existing literature, we show that this test is well suited for event studies based on time-series data.…
Randomization testing is a fundamental method in statistics, enabling inferential tasks such as testing for (conditional) independence of random variables, constructing confidence intervals in semiparametric location models, and…
We consider the problem of comparing probability densities between two groups. A new probabilistic tensor product smoothing spline framework is developed to model the joint density of two variables. Under such a framework, the probability…
We study properties of two resampling scenarios: Conditional Randomisation and Conditional Permutation schemes, which are relevant for testing conditional independence of discrete random variables $X$ and $Y$ given a random variable $Z$.…
In this paper, we revisit the classical goodness-of-fit problems for univariate distributions; we propose a new testing procedure based on a characterisation of the uniform distribution. Asymptotic theory for the simple hypothesis case is…
Existing two-sample testing techniques, particularly those based on choosing a kernel for the Maximum Mean Discrepancy (MMD), often assume equal sample sizes from the two distributions. Applying these methods in practice can require…
We propose a general new method, the conditional permutation test, for testing the conditional independence of variables $X$ and $Y$ given a potentially high-dimensional random vector $Z$ that may contain confounding factors. The proposed…
Conformalized multiple testing offers a model-free way to control predictive uncertainty in decision-making. Existing methods typically use only part of the available data to build score functions tailored to specific settings. We propose a…
Throughout the last decade, random forests have established themselves as among the most accurate and popular supervised learning methods. While their black-box nature has made their mathematical analysis difficult, recent work has…
Vast literature on experimental design extends from Fisher and Snedecor to the modern day. When data lies beyond the assumption of univariate normality, nonparametric methods including rank based statistics and permutation tests are…
Consider a population consisting of clusters of sampling units, evolving temporally, spatially, or according to other dynamics. We wish to monitor the evolution of its means, medians, or other parameters. For administrative convenience and…