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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…
One can consider $\mu$-Martin-L\"of randomness for a probability measure $\mu$ on $2^{\omega}$, such as the Bernoulli measure $\mu_p$ given $p \in (0, 1)$. We study Bernoulli randomness of sequences in $n^{\omega}$ with parameters $p_0,…
Multi-armed bandit algorithms have been argued for decades as useful for adaptively randomized experiments. In such experiments, an algorithm varies which arms (e.g. alternative interventions to help students learn) are assigned to…
A multi-armed bandit with finitely many arms is studied when each arm is a homogeneous Markov process on an underlying finite state space. The transition law of one of the arms, referred to as the odd arm, is different from the common…
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.…
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…
In this paper, we consider the fundamental problem of testing for monotone trend in a time series. While the term "trend" is commonly used and has an intuitive meaning, it is first crucial to specify its exact meaning in a hypothesis…
In observational studies of discrimination, the most common statistical approaches consider either the rate at which decisions are made (benchmark tests) or the success rate of those decisions (outcome tests). Both tests, however, have…
In this work we address the problem of detecting whether a sampled probability distribution of a random variable $V$ has infinite first moment. This issue is notably important when the sample results from complex numerical simulation…
A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…
Many experiments are concerned with the comparison of counts between treatment groups. Examples include the number of successful signups in conversion rate experiments, or the number of errors produced by software versions in canary…
We shall show in this paper that there are experiments which are Bernoulli trials with success probability p > 0.5, and which have the curious feature that it is possible to correctly predict the outcome with probability > p.
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…
Let $\pi_n$ be a uniformly chosen random permutation on $[n]$. Using an analysis of the probability that two overlapping consecutive $k$-permutations are order isomorphic, the authors of a recent paper showed that the expected number of…
The last success problem is an optimal stopping problem that aims to maximize the probability of stopping on the last success in a sequence of independent $n$ Bernoulli trials. In the classical setting where complete information about the…
Thompson sampling (TS) is widely used for stochastic multi-armed bandits, yet its inferential properties under adaptive data collection are subtle. Classical asymptotic theory for sample means can fail because arm-specific sample sizes are…
In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…
A Bernoulli random walk is a random trajectory starting from 0 and having i.i.d. increments, each of them being $+1$ or -1, equally likely. The other families cited in the title are Bernoulli random walks under various conditionings. A peak…
Adaptive sampling schemes are well known to create complex dependence that may invalidate conventional inference methods. A recent line of work shows that this need not be the case for UCB-type algorithms in multi-armed bandits. A central…
Variational inequalities have gained significant attention in machine learning and optimization research. While stochastic methods for solving these problems typically assume independent data sampling, we investigate an alternative approach…