Related papers: Gaussian Universal Likelihood Ratio Testing
In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…
The problem of testing the goodness of fit of an absolutely continuous distribution to a set of observations grouped into equal probability intervals, against to a family of sequences of alternatives approaching the hypothesis is…
There are many high dimensional function classes that have fast agnostic learning algorithms when assumptions on the distribution of examples can be made, such as Gaussianity or uniformity over the domain. But how can one be confident that…
Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…
This paper proposes a unified framework to quantify local and global inferential uncertainty for high dimensional nonparanormal graphical models. In particular, we consider the problems of testing the presence of a single edge and…
Hotelling's T-squared test is a classical tool to test if the normal mean of a multivariate normal distribution is a specified one or the means of two multivariate normal means are equal. When the population dimension is higher than the…
Hypothesis testing is a useful statistical tool in determining whether a given model should be rejected based on a sample from the population. Sample data may contain sensitive information about individuals, such as medical information.…
In this paper, we consider testing the martingale difference hypothesis for high-dimensional time series. Our test is built on the sum of squares of the element-wise max-norm of the proposed matrix-valued nonlinear dependence measure at…
Quantum hypothesis testing (QHT) concerns the statistical inference of unknown quantum states. In the general setting of composite hypotheses, the goal of QHT is to determine whether an unknown quantum state belongs to one or another of two…
Statistical divergences are ubiquitous in machine learning as tools for measuring discrepancy between probability distributions. As these applications inherently rely on approximating distributions from samples, we consider empirical…
We introduce a new procedure for testing the significance of a set of regression coefficients in a Gaussian linear model with $n \geq d$. Our method, the $L$-test, provides the same statistical validity guarantee as the classical $F$-test,…
We study the Gaussian sequence model, i.e. $X \sim N(\mathbf{\theta}, I_\infty)$, where $\mathbf{\theta} \in \Gamma \subset \ell_2$ is assumed to be convex and compact. We show that goodness-of-fit testing sample complexity is lower bounded…
We propose the Generalized Probabilistic U-Net, which extends the Probabilistic U-Net by allowing more general forms of the Gaussian distribution as the latent space distribution that can better approximate the uncertainty in the reference…
\cite{tsagris2025a} proposed the generalized circular projected Cauchy (GCPC) distribution, whose special case is the wrapped Cauchy distribution. In this paper we first derive the relationship with the wrapped Cauchy distribution, and then…
Graphical and sparse (inverse) covariance models have found widespread use in modern sample-starved high dimensional applications. A part of their wide appeal stems from the significantly low sample sizes required for the existence of…
In this paper, we consider the sphericity test for a one-sample problem under high-dimensional two-step monotone incomplete data. Existing asymptotic expansions for the null distributions of the likelihood ratio test (LRT) statistic and…
We consider Bayesian multiple statistical classification problem in the case where the unknown source distributions are estimated from the labeled training sequences, then the estimates are used as nominal distributions in a robust…
I propose two U-statistics to test coefficients in generalized linear models. One of them is used to deal with global hypothesis and the other one to test with the nuisance parameter. Both the statistics proposed are within high-dimensional…
Certifiable, adaptive uncertainty estimates for unknown quantities are an essential ingredient of sequential decision-making algorithms. Standard approaches rely on problem-dependent concentration results and are limited to a specific…
The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…