Related papers: Testing randomness
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
Given a positive random variable $X$, $X\ge0$ a.s., a null hypothesis $H_0:E(X)\le\mu$ and a random sample of infinite size of $X$, we construct test supermartingales for $H_0$, i.e. positive processes that are supermartingale if the null…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…
Conformal inference is a fundamental and versatile tool that provides distribution-free guarantees for many machine learning tasks. We consider the transductive setting, where decisions are made on a test sample of $m$ new points, giving…
This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical…
This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty…
We propose a nonparametric sequential test that aims to address two practical problems pertinent to online randomized experiments: (i) how to do a hypothesis test for complex metrics; (ii) how to prevent type $1$ error inflation under…
While the traditional viewpoint in machine learning and statistics assumes training and testing samples come from the same population, practice belies this fiction. One strategy -- coming from robust statistics and optimization -- is thus…
We present a randomization-based inferential framework for experiments characterized by a strongly ignorable assignment mechanism where units have independent probabilities of receiving treatment. Previous works on randomization tests often…
This paper argues for a wider use of the functional theory of randomness, a modification of the algorithmic theory of randomness getting rid of unspecified additive constants. Both theories are useful for understanding relationships between…
We extend conformal inference to general settings that allow for time series data. Our proposal is developed as a randomization method and accounts for potential serial dependence by including block structures in the permutation scheme. As…
Marginal structural models were introduced in order to provide estimates of causal effects from interventions based on observational studies in epidemiological research. The key point is that this can be understood in terms of Girsanov's…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper…
Reliable inference for spatial regression remains challenging because it requires the correct specification of the spatial dependence structure, the mean trend, and the error distribution. Existing parametric testing methods rely on…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define several notions of randomness associated with interval, rather than precise,…
We consider the problem of inference in shift-share research designs. The choice between existing approaches that allow for unrestricted spatial correlation involves tradeoffs, varying in terms of their validity when there are relatively…
Machine learning systems deployed in the real world must operate under dynamic and often unpredictable distribution shifts. This challenges the validity of statistical safety assurances on the system's risk established beforehand. Common…
This paper considers a problem of distributed hypothesis testing and social learning. Individual nodes in a network receive noisy local (private) observations whose distribution is parameterized by a discrete parameter (hypotheses). The…
The aim of this paper is to propose a methodology for testing general hypothesis in a Markovian setting with random sampling. A discrete Markov chain X is observed at random time intervals $\tau$ k, assumed to be iid with unknown…