Related papers: E-values and sequential power-one tests for monoto…
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…
We investigate the property for an input-output system to map unimodal inputs to unimodal outputs. As a first step, we analyse this property for linear time-invariant (LTI) systems, static nonlinearities, and interconnections of those. In…
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 develop the theory of hypothesis testing based on the e-value, a notion of evidence that, unlike the p-value, allows for effortlessly combining results from several studies in the common scenario where the decision to perform a new study…
We develop E-variables for testing whether two or more data streams come from the same source or not, and more generally, whether the difference between the sources is larger than some minimal effect size. These E-variables lead to exact,…
We introduce the E-measure: a measure-like generalization of the E-value to a class of hypotheses. Unlike classical measures, E-measures are closed under infimums instead of addition. They arise from a compatibility axiom with logical…
We introduce a testing-by-betting framework that leverages predictions on unlabeled data to enhance the power of sequential hypothesis testing. Given limited samples from the joint distribution of $(X,Y)$, and additional unlabeled samples…
Sequential monitoring of randomized trials traditionally relies on parametric assumptions or asymptotic approximations. We discuss a family of nonparametric sequential tests - collectively called e-RT - for binary, event-only, and…
There is a useful counterpart of conformal prediction for e-values, called conformal e-prediction. Conformal prediction can serve as basis for testing the assumption of exchangeability, leading to conformal testing. Similarly, conformal…
The notion of an e-value has been recently proposed as a possible alternative to critical regions and p-values in statistical hypothesis testing. In this paper we consider testing the nonparametric hypothesis of symmetry, introduce…
E-variables are tools for retaining type-I error guarantee with optional stopping. We extend E-variables for sequential two-sample tests to general null hypotheses and anytime-valid confidence sequences. We provide implementations for…
Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors,…
We propose a sequential, anytime-valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood…
E-variables are a relatively new approach for testing statistical hypotheses that has been experiencing major development during the last several years. In this paper we introduce the method of e-variable-approximability and use it to…
Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper…
We address the problem of testing for the invariance of a probability measure under the action of a group of linear transformations. We propose a procedure based on consideration of one-dimensional projections, justified using a variant of…
Adaptive clinical trials rely on interim analyses, flexible stopping, and data-dependent design modifications that complicate statistical guarantees when fixed-horizon test statistics are repeatedly inspected or reused after adaptations.…
The t-statistic is a widely-used scale-invariant statistic for testing the null hypothesis that the mean is zero. Martingale methods enable sequential testing with the t-statistic at every sample size, while controlling the probability of…
E-values offer a powerful framework for aggregating evidence across different (possibly dependent) statistical experiments. A fundamental question is to identify e-merging functions, namely mappings that merge several e-values into a single…
Compared to p-values, e-values provably guarantee safe, valid inference. If the goal is to test multiple hypotheses simultaneously, one can construct e-values for each individual test and then use the recently developed e-BH procedure to…