Related papers: The Impossibility Region for Detecting Sparse Mixt…
Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…
The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null…
We study a large-scale one-sided multiple testing problem in which test statistics follow normal distributions with unit variance, and the goal is to identify signals with positive mean effects. A conventional approach is to compute…
Global hypothesis tests are a useful tool in the context of, e.g, clinical trials, genetic studies or meta analyses, when researchers are not interested in testing individual hypotheses, but in testing whether none of the hypotheses is…
Pairs of states, or "boxes" are the basic objects in the resource theory of asymmetric distinguishability (Wang and Wilde, 2019), where free operations are arbitrary quantum channels that are applied to both states. From this point of view,…
We study the rate of decay of the probability of error for distinguishing between a sparse signal with noise, modeled as a sparse mixture, from pure noise. This problem has many applications in signal processing, evolutionary biology,…
In science, the most widespread statistical quantities are perhaps $p$-values. A typical advice is to reject the null hypothesis $H_0$ if the corresponding p-value is sufficiently small (usually smaller than 0.05). Many criticisms regarding…
The likelihood ratio statistic, with its asymptotic $\chi^2$ distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be $\chi^2$, as…
We present a general nonparametric approach for testing whether a statistical parameter defined through conditional distributions is constant across the conditioning variables. Such hypotheses arise naturally in problems such as assessing…
We consider nonparametric sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution with some loose constraints. We…
We study the problem of recovering a hidden binary $k$-sparse $p$-dimensional vector $\beta$ from $n$ noisy linear observations $Y=X\beta+W$ where $X_{ij}$ are i.i.d. $\mathcal{N}(0,1)$ and $W_i$ are i.i.d. $\mathcal{N}(0,\sigma^2)$. A…
We propose a new method to define anomaly scores and apply this to particle physics collider events. Anomalies can be either rare, meaning that these events are a minority in the normal dataset, or different, meaning they have values that…
High dimensional hypothesis test deals with models in which the number of parameters is significantly larger than the sample size. Existing literature develops a variety of individual tests. Some of them are sensitive to the dense and small…
Studying the effects of one-way variation of any number of parameters on any number of output probabilities quickly becomes infeasible in practice, especially if various evidence profiles are to be taken into consideration. To provide for…
We study the problem of detecting the presence of a single unknown spike in a rectangular data matrix, in a high-dimensional regime where the spike has fixed strength and the aspect ratio of the matrix converges to a finite limit. This…
Estimation of the proportion of null hypotheses in a multiple testing problem can greatly enhance the performance of the existing algorithms. Although various estimators for the proportion of null hypotheses have been proposed, most are…
Dark matter candidates arising in models of particle physics incorporating weak scale supersymmetry may produce detectable signals through their annihilation into neutrinos, photons, or positrons. A large number of relevant experiments are…
This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite-dimensional nuisance parameter. We introduce a…
We develop a new test of local bias, by constructing a locally biased halo density field from sampling the dark matter-halo distribution. Our test differs from conventional tests in that it preserves the full scatter in the bias relation…
This paper develops a general framework for conducting inference on the rank of an unknown matrix $\Pi_0$. A defining feature of our setup is the null hypothesis of the form $\mathrm H_0: \mathrm{rank}(\Pi_0)\le r$. The problem is of first…