Related papers: Optimal E-Values for Exponential Families: the Sim…
We develop the theory of hypothesis testing based on the e-value, a notion of evidence that, unlike the p-value, allows for effortlessly combining results from several studies in the common scenario where the decision to perform a new study…
We consider testing a composite null hypothesis $\mathcal{P}$ against a point alternative $\mathsf{Q}$ using e-variables, which are nonnegative random variables $X$ such that $\mathbb{E}_\mathsf{P}[X] \leq 1$ for every $\mathsf{P} \in…
We start from a parametrized system of $d$ generalized polynomial equations (with real exponents) for $d$ positive variables, involving $n$ generalized monomials with $n$ positive parameters. Existence and uniqueness of a solution for all…
The main purpose of this paper is to introduce first a new family of empirical test statistics for testing a simple null hypothesis when the vector of parameters of interest are defined through a specific set of unbiased estimating…
We develop e-values and e-processes testing the null hypothesis that a distribution over nonnegative integers is monotone, and that a distribution over integers is unimodal given a certain mode. Our e-processes lead to tests of power one…
One-parameter natural exponential family (NEF) plays fundamental roles in probability and statistics. This article contains two independent results: (a) A conjecture of Bar-Lev, Bshouty and Enis states that a polynomial with a simple root…
In this paper we study a class of exponential family on permutations, which includes some of the commonly studied Mallows models. We show that the pseudo-likelihood estimator for the natural parameter in the exponential family is…
Hypothesis testing and other statistical inference procedures are most efficient when a reliable low-dimensional parametric family can be specified. We propose a method that learns such a family when one exists but its form is not known a…
We study worst-case-growth-rate-optimal (GROW) e-statistics for hypothesis testing between two group models. It is known that under a mild condition on the action of the underlying group G on the data, there exists a maximally invariant…
Semiparametric exponential family proposed by Ning et al. (2017) is an extension of the parametric exponential family to the case with a nonparametric base measure function. Such a distribution family has potential application in some areas…
In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…
We develop an analog of the exponential families of Wilf in which the label sets are finite dimensional vector spaces over a finite field rather than finite sets of positive integers. The essential features of exponential families are…
We introduce the E-measure: a measure-like generalization of the E-value to a class of hypotheses. Unlike classical measures, E-measures are closed under infimums instead of addition. They arise from a compatibility axiom with logical…
Statistical hypothesis testing, as formalized by 20th Century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in…
New families of $E$-functions are described in the context of the compact simple Lie groups O(5) and G(2). These functions of two real variables generalize the common exponential functions and for each group, only one family is currently…
We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…
Exponential families of discrete probability distributions when the normalizing constant (or overall effect) is added or removed are compared in this paper. The latter setup, in which the exponential family is curved, is particularly…
We introduce Exponential Family Discriminant Analysis (EFDA), a unified generative framework that extends classical Linear Discriminant Analysis (LDA) beyond the Gaussian setting to any member of the exponential family. Under the assumption…
Probability forecasts for binary events play a central role in many applications. Their quality is commonly assessed with proper scoring rules, which assign forecasts a numerical score such that a correct forecast achieves a minimal…
Bayes' rule describes how to infer posterior beliefs about latent variables given observations, and inference is a critical step in learning algorithms for latent variable models (LVMs). Although there are exact algorithms for inference and…