Related papers: Unique Distributions Under Non-IID Assumption

Non-uniform estimates are obtained for Poisson, compound Poisson, translated Poisson, negative binomial and binomial approximations to sums of of m-dependent integer-valued random variables. Estimates for Wasserstein metric also follow…

Mixture distributions are extensively used as a modeling tool in diverse areas from machine learning to communications engineering to physics, and obtaining bounds on the entropy of probability distributions is of fundamental importance in…

We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint…

Scientific knowledge expands by observing the world, hypothesizing some theories about it, and testing them against collected data. When those theories take the form of statistical models, statistical analyses are involved in the process of…

Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new…

In multisite trials, researchers are often interested in several inferential goals: estimating treatment effects for each site, ranking these effects, and studying their distribution. This study seeks to identify optimal methods for…

Statistical modeling plays a fundamental role in understanding the underlying mechanism of massive data (statistical inference) and predicting the future (statistical prediction). Although all models are wrong, researchers try their best to…

Predictions of uncertainty-aware models are diverse, ranging from single point estimates (often averaged over prediction samples) to predictive distributions, to set-valued or credal-set representations. We propose a novel unified…

This paper considers the problem of design-based inference for the average treatment effect in finely stratified experiments. Here, by "design-based'' we mean that the only source of uncertainty stems from the randomness in treatment…

In this paper we introduce a new class of multivariate unimodal distributions, motivated by Khintchine's representation. We start by proposing a univariate model, whose support covers all the unimodal distributions on the real line. The…

We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from $s$ distributions, $p_1, p_2, \ldots, p_s$, we design testers for the…

Nested sampling has emerged as a valuable tool for Bayesian analysis, in particular for determining the Bayesian evidence. The method is based on a specific type of random sampling of the likelihood function and prior volume of the…

In natural phenomena, data distributions often deviate from normality. One can think of cataclysms as a self-explanatory example: events that occur almost never, and at the same time are many standard deviations away from the common…

In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…

In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…

Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…

We derive expressions for the finite-sample distribution of the Lasso estimator in the context of a linear regression model in low as well as in high dimensions by exploiting the structure of the optimization problem defining the estimator.…

For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as…

The paper aims at finding widely and smoothly defined nonparametric location and scatter functionals. As a convenient vehicle, maximum likelihood estimation of the location vector m and scatter matrix S of an elliptically symmetric t…

Many functionals of interest in statistics and machine learning can be written as minimizers of expected loss functions. Such functionals are called $M$-estimands, and can be estimated by $M$-estimators -- minimizers of empirical average…