Related papers: Universal and Composite Hypothesis Testing via Mis…
Universal hypothesis testing refers to the problem of deciding whether samples come from a nominal distribution or an unknown distribution that is different from the nominal distribution. Hoeffding's test, whose test statistic is equivalent…
Hoeffding's formulation and solution to the universal hypothesis testing (UHT) problem had a profound impact on many subsequent works dealing with asymmetric hypotheses. In this work, we introduce a quantum universal hypothesis testing…
We consider a binary statistical hypothesis testing problem, where $n$ independent and identically distributed random variables $Z^n$ are either distributed according to the null hypothesis $P$ or the alternate hypothesis $Q$, and only $P$…
Consider a binary statistical hypothesis testing problem, where $n$ independent and identically distributed random variables $Z^n$ are either distributed according to the null hypothesis $P$ or the alternative hypothesis $Q$, and only $P$…
This paper concerns the construction of tests for universal hypothesis testing problems, in which the alternate hypothesis is poorly modeled and the observation space is large. The mismatched universal test is a feature-based technique for…
This paper is devoted to the study of the general linear hypothesis testing (GLHT) problem of multi-sample high-dimensional mean vectors. For the GLHT problem, we introduce a test statistic based on $L^2$-norm and random integration method,…
We propose a general method for constructing hypothesis tests and confidence sets that have finite sample guarantees without regularity conditions. We refer to such procedures as "universal." The method is very simple and is based on a…
In this paper, for the problem of heteroskedastic general linear hypothesis testing (GLHT) in high-dimensional settings, we propose a random integration method based on the reference L2-norm to deal with such problems. The asymptotic…
The classical likelihood ratio test (LRT) based on the asymptotic chi-squared distribution of the log likelihood is one of the fundamental tools of statistical inference. A recent universal LRT approach based on sample splitting provides…
This paper investigates improved testing inferences under a general multivariate elliptical regression model. The model is very flexible in terms of the specification of the mean vector and the dispersion matrix, and of the choice of the…
We consider a distributed detection problem where measurements at each sensor follow a general parametric distribution. The network does not have a central processing unit or fusion center (FC). Thus, each node takes some measurements, does…
This paper studies recursive composite hypothesis testing in a network of sparsely connected agents. The network objective is to test a simple null hypothesis against a composite alternative concerning the state of the field, modeled as a…
We study the problem of mismatched binary hypothesis testing between i.i.d. distributions. We analyze the tradeoff between the pairwise error probability exponents when the actual distributions generating the observation are different from…
We study a variant of the simple hypothesis testing problem where observed samples do not necessarily come from either of the specified distributions, but rather from a close variant of them. In this setting, we require a test that is…
This paper adresses the problem of testing for the equality of $k$ probability distributions on Hilbert spaces, with $k\geqslant 2$. We introduce a generalization of the maximum variance discrepancy called multiple maximum variance…
Calibration of mean estimates for predictions is a crucial property in many applications, particularly in the fields of financial and actuarial decision-making. In this paper, we first review classical approaches for validating…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
We propose a universal classifier for binary Neyman-Pearson classification where null distribution is known while only a training sequence is available for the alternative distribution. The proposed classifier interpolates between…
We interpret likelihood-based test functions from a geometric perspective where the Kullback-Leibler (KL) divergence is adopted to quantify the distance from a distribution to another. Such a test function can be seen as a sub-Gaussian…
Outlier hypothesis testing is studied in a universal setting. Multiple sequences of observations are collected, a small subset of which are outliers. A sequence is considered an outlier if the observations in that sequence are distributed…