Related papers: When Are Trade-Off Functions Testable from Finite …
There exist a number of tests for assessing the nonparametric heteroscedastic location-scale assumption. Here we consider a goodness-of-fit test for the more general hypothesis of the validity of this model under a parametric functional…
Permutation tests are a powerful and flexible approach to inference via resampling. As computational methods become more ubiquitous in the statistics curriculum, use of permutation tests has become more tractable. At the heart of the…
The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…
In this paper we revisit the binary hypothesis testing problem with one-sided compression. Specifically we assume that the distribution in the null hypothesis is a mixture distribution of iid components. The distribution under the…
Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…
This paper studies distribution-free inference in settings where the data set has a hierarchical structure -- for example, groups of observations, or repeated measurements. In such settings, standard notions of exchangeability may not hold.…
We consider the problem of testing whether two finite-dimensional random dot product graphs have generating latent positions that are independently drawn from the same distribution, or distributions that are related via scaling or…
In classical statistics, the bias-variance trade-off describes how varying a model's complexity (e.g., number of fit parameters) affects its ability to make accurate predictions. According to this trade-off, optimal performance is achieved…
The composite binary hypothesis testing problem within the Neyman-Pearson framework is considered. The goal is to maximize the expectation of a nonlinear function of the detection probability, integrated with respect to a given probability…
In scientific studies involving analyses of multivariate data, basic but important questions often arise for the researcher: Is the sample exchangeable, meaning that the joint distribution of the sample is invariant to the ordering of the…
Randomization tests deliver exact finite-sample Type 1 error control when the null satisfies the randomization hypothesis. In practice, achieving these guarantees often requires stronger conditions than the null hypothesis of primary…
Split conformal prediction has recently sparked great interest due to its ability to provide formally guaranteed uncertainty sets or intervals for predictions made by black-box neural models, ensuring a predefined probability of containing…
In this work, we revisit the one- and two-sample testing problems: binary hypothesis testing in which one or both distributions are unknown. For the one-sample test, we provide a more streamlined proof of the asymptotic optimality of…
Conformal prediction is a distribution-free uncertainty quantification method that has gained popularity in the machine learning community due to its finite-sample guarantees and ease of use. Its most common variant, dubbed split conformal…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…
In this work we establish an algorithm and distribution independent non-asymptotic trade-off between the model size, excess test loss, and training loss of linear predictors. Specifically, we show that models that perform well on the test…
The problem of zero-rate multiterminal hypothesis testing is revisited from the perspective of information-spectrum approach and finite blocklength analysis. A Neyman-Pearson-like test is proposed and its non-asymptotic performance is…
Using cumulative residual processes, we propose joint goodness-of-fit tests for conditional means and variances functions in the context of nonlinear time series with martingale difference innovations. The main challenge comes from the fact…
In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…
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…