Related papers: A Finite-Sample Strong Converse for Binary Hypothe…
This paper characterizes the optimal type-II error exponent for a distributed hypothesis testing-against-independence problem when the \emph{expected} rate of the sensor-detector link is constrained. Unlike for the well-known…
In this article, we investigate posterior convergence of nonparametric binary and Poisson regression under possible model misspecification, assuming general stochastic process prior with appropriate properties. Our model setup and objective…
In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…
We consider the problem of distilling uniform random bits from an unknown source with a given $p$-entropy using linear hashing. As our main result, we estimate the expected $p$-divergence from the uniform distribution over the ensemble of…
We investigate the large-time asymptotics of nonlinear diffusion equations $u_t = \Delta u^p$ in dimension $n \ge 1$, in the exponent interval $p > n/(n+2)$, when the initial datum $u_0$ is of bounded second moment. Precise rates of…
The composite binary hypothesis testing problem within the Neyman-Pearson framework is considered. The goal is to maximize the expectation of a nonlinear function of the detection probability, integrated with respect to a given probability…
The minimax robust hypothesis testing problem for the case where the nominal probability distributions are subject to both modeling errors and outliers is studied in twofold. First, a robust hypothesis testing scheme based on a relative…
We propose a new definition of the chi-square divergence between distributions. Based on convexity properties and duality, this version of the {\chi}^2 is well suited both for the classical applications of the {\chi}^2 for the analysis of…
We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…
Consider the sequential testing of binary outcomes. The a posteriori belief process and its objective conditional-probability counterpart generally differ but converge to the same result in well-defined tests. We show that unless the two…
In this paper we consider, in the general context of CAT(0) spaces, an iterative schema which alternates between Halpern and Krasnoselskii-Mann style iterations. We prove, under suitable conditions, the strong convergence of this algorithm,…
The binary divergences that are divergences between probability measures defined on the same 2-point set have an interesting property. For the chi-squared divergence and the relative entropy, it is known that their binary divergence attain…
This paper proposes a framework for semantic hypothesis testing tailored to imaging inverse problems. Modern imaging methods struggle to support hypothesis testing, a core component of the scientific method that is essential for the…
We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Specifically, we…
We consider the problem of constructing confidence intervals (CIs) for the population mean of $N$ values $\{x_1, \ldots, x_N\} \subset \Sigma^N$ based on a random sample of size $n$, denoted by $X^n \equiv (X_1, \ldots, X_n)$, drawn…
For any pair of quantum states (the hypotheses), the task of binary quantum hypotheses testing is to derive the tradeoff relation between the probability $p_{01}$ of rejecting the null hypothesis and $p_{10}$ of accepting the alternative…
This paper deals with measuring the Bayesian robustness of classes of contaminated priors. Two different classes of priors in the neighborhood of the elicited prior are considered. The first one is the well-known $\epsilon$-contaminated…
We introduce two novel non-parametric statistical hypothesis tests. The first test, called the relative test of dependency, enables us to determine whether one source variable is significantly more dependent on a first target variable or a…
We consider the group testing problem, in which one seeks to identify a subset of defective items within a larger set of items based on a number of noisy tests. While matching achievability and converse bounds are known in several cases of…
An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.