相关论文: More Efficient Exact Group-Invariance Testing: usi…
Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…
It is conventionally believed that a permutation test should ideally use all permutations. If this is computationally unaffordable, it is believed one should use the largest affordable Monte Carlo sample or (algebraic) subgroup of…
We study e-values for quantifying evidence against exchangeability and general invariance of a random variable under a compact group. We start by characterizing such e-values, and explaining how they nest traditional group invariance 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…
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…
We propose the density ratio permutation test, a hypothesis test that assesses whether the ratio between two densities is proportional to a known function based on independent samples from each distribution. The test uses an efficient…
Invariant and equivariant models incorporate the symmetry of an object to be estimated (here non-parametric regression functions $f : \mathcal{X} \rightarrow \mathbb{R}$). These models perform better (with respect to $L^2$ loss) and are…
Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence…
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…
Permutation tests date back nearly a century to Fisher's randomized experiments, and remain an immensely popular statistical tool, used for testing hypotheses of independence between variables and other common inferential questions. Much of…
We review approaches to statistical inference based on randomization. Permutation tests are treated as an important special case. Under a certain group invariance property, referred to as the ``randomization hypothesis,'' randomization…
Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…
Consider two random variables contaminated by two unknown transformations. The aim of this paper is to test the equality of those transformations. Two cases are distinguished: first, the two random variables have known distributions.…
The relationship between mappings of sets and renormalization group transformations is established, and renormalization group invariants of such mappings are found. These results are valid both for continuous and discrete mappings and for…
We develop anytime-valid tests of invariance under the action of compact groups. The resulting test statistics are optimal in a logarithmic-growth sense. We apply our method to extend recent anytime-valid tests of independence and to…
We identify a recently proposed shifting operation on classical phase space as a gauge transformation for statistical mechanical microstates. The infinitesimal generators of the continuous gauge group form a non-commutative Lie algebra,…
Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…
Measuring the effect of peers on individuals' outcomes is a challenging problem, in part because individuals often select peers who are similar in both observable and unobservable ways. Group formation experiments avoid this problem by…
In multigroup data settings with small within-group sample sizes, standard $F$-tests of group-specific linear hypotheses can have low power, particularly if the within-group sample sizes are not large relative to the number of explanatory…
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…