Related papers: Nonasymptotic one-and two-sample tests in high dim…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence…
In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…
We observe $n$ independent $p-$dimensional Gaussian vectors with missing coordinates, that is each value (which is assumed standardized) is observed with probability $a>0$. We investigate the problem of minimax nonparametric testing that…
A pair of probability distributions over $\{0,1\}^n$ is said to be $(k,\delta)$-wise indistinguishable if all of the size $k$ marginals are within statistical distance at most $\delta$. Previous works introduced this concept and study when…
Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number of tests required for high-probability recovery in the sublinear regime $k = n^{\theta}$ (with $\theta \in (0,1)$), with…
Due to their parsimony, separable covariance models have been popular in modeling matrix-variate data. However, the inference from such a model may be misleading if the population covariance matrix $\Sigma$ is actually non-separable,…
This work is concerned with the detection of a mixture distribution from a $\mathbb{R}$-valued sample. Given a sample $X_1,\dots,X_n$ and an even density $\phi$, our aim is to detect whether the sample distribution is $\phi(\cdot-\mu)$ for…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
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…
The assumption of separability of the covariance operator for a random image or hypersurface can be of substantial use in applications, especially in situations where the accurate estimation of the full covariance structure is unfeasible,…
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…
We consider the problem of sparsity testing in the high-dimensional linear regression model. The problem is to test whether the number of non-zero components (aka the sparsity) of the regression parameter $\theta^*$ is less than or equal to…
We study the problem of nonparametric two-sample testing using the sliced Wasserstein (SW) distance. While prior theoretical and empirical work indicates that the SW distance offers a promising balance between strong statistical guarantees…
A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally n sequences with s anomalous sequences to be detected. Each typical sequence contains m independent and identically distributed (i.i.d.)…
We consider composite-composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a convex subset $\mathcal{C}$ of $\mathbb{R}^d$. We adopt a minimax point of view and our primary…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional condition on its rate of increase compared to the sample size. On the…
We apply FDR thresholding to a non-Gaussian vector whose coordinates X_i, i=1,..., n, are independent exponential with individual means $\mu_i$. The vector $\mu =(\mu_i)$ is thought to be sparse, with most coordinates 1 but a small fraction…
We study properties of a sample covariance estimate $\widehat \Sigma$ given a finite sample of $n$ i.i.d. centered random elements in $\R^d$ with the covariance matrix $\Sigma$. We derive dimension-free bounds on the squared Frobenius norm…
Nonparametric two sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is…