Related papers: Testing for unspecified periodicities in binary ti…
We consider statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses, under the assumption that a suitable single test (and corresponding $p$-value) is known for each…
We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…
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…
Two-sided statistical tests and p-values are well defined only when the test statistic in question has a symmetric distribution. A new two-sided p-value called conditional p-value $P_C$ is introduced here. It is closely related to the…
We introduce a new statistical test based on the observed spacings of ordered data. The statistic is sensitive to detect non-uniformity in random samples, or short-lived features in event time series. Under some conditions, this new test…
Fisher's likelihood is widely used for statistical inference for fixed unknowns. This paper aims to extend two important likelihood-based methods, namely the maximum likelihood procedure for point estimation and the confidence procedure for…
This paper introduces a statistical test inferring whether a variable allows separating two classes by means of a single critical value. Its test statistic is the prediction error of a nonparametric threshold classifier. While this approach…
We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test under the generalized Neyman-Pearson criterion. In outlier hypothesis testing, one is given multiple…
Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability…
We consider goodness-of-fit tests with i.i.d. samples generated from a categorical distribution $(p_1,...,p_k)$. For a given $(q_1,...,q_k)$, we test the null hypothesis whether $p_j=q_{\pi(j)}$ for some label permutation $\pi$. The…
We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical…
Given a discrete-valued sample $X_1,...,X_n$ we wish to decide whether it was generated by a distribution belonging to a family $H_0$, or it was generated by a distribution belonging to a family $H_1$. In this work we assume that all…
Binary classification is a task that involves the classification of data into one of two distinct classes. It is widely utilized in various fields. However, conventional classifiers tend to make overconfident predictions for data that…
Let $\{X_n\}_{n=0}^{\infty}$ be a stationary real-valued time series with unknown distribution. Our goal is to estimate the conditional expectation of $X_{n+1}$ based on the observations $X_i$, $0\le i\le n$ in a strongly consistent way.…
We consider the problem of sequentially testing for changes in the mean parameter of a time series, compared to a benchmark period. Most tests in the literature focus on the null hypothesis of a constant mean versus the alternative of a…
Causal inference in completely randomized treatment-control studies with binary outcomes is discussed from Fisherian, Neymanian and Bayesian perspectives, using the potential outcomes framework. A randomization-based justification of…
We propose a new algorithmic framework for sequential hypothesis testing with i.i.d. data, which includes A/B testing, nonparametric two-sample testing, and independence testing as special cases. It is novel in several ways: (a) it takes…
A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…
We study the identification of direct and indirect causes on time series and provide conditions in the presence of latent variables, which we prove to be necessary and sufficient under some graph constraints. Our theoretical results and…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…