Related papers: Coverage Probability of Random Intervals
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
A confidence distribution is a complete tool for making frequentist inference for a parameter of interest $\psi$ based on an assumed parametric model. Indeed, it allows to reach point estimates, to assess their precision, to set up tests…
In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the…
We consider a linear regression model, with the parameter of interest a specified linear combination of the regression parameter vector. We suppose that, as a first step, a data-based model selection (e.g. by preliminary hypothesis tests or…
Many existing approaches for estimating parameters in settings with distributional shifts operate under an invariance assumption. For example, under covariate shift, it is assumed that $p(y|x)$ remains invariant. We refer to such…
Information and uncertainty are closely related and extensively studied concepts in a number of scientific disciplines such as communication theory, probability theory, and statistics. Increasing the information arguably reduces the…
The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when…
This paper develops an intuitive concept of perfect dependence between two variables of which at least one has a nominal scale. Perfect dependence is attainable for all marginal distributions. It furthermore proposes a set of dependence…
The variance of primes in short intervals relates to the Riemann Hypothesis, Montgomery's Pair Correlation Conjecture and the Hardy--Littlewood Conjecture. In regards to its asymptotics, very little is known unconditionally. We study the…
An important problem in statistics is the construction of confidence regions for unknown parameters. In most cases, asymptotic distribution theory is used to construct confidence regions, so any coverage probability claims only hold…
We introduce new method for generating correlated or uncorrelated Bernoulli random variables by using the binary expansion of a continuous random variable with support on the unit interval. We show that when this variable has a symmetric…
We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially…
In this paper we study the probability that a $d$ dimensional simple random walk (or the first $L$ steps of it) covers each point in a nearest neighbor path connecting 0 and the boundary of an $L_1$ ball. We show that among all such paths,…
Let $A$ be a compact $d$-dimensional $C^2$ Riemannian manifold with boundary, embedded in ${\bf R}^m$ where $m \geq d \geq 2$, and let $B$ be a nice subset of $A$ (possibly $B=A$). Let $X_1,X_2, \ldots $ be independent random uniform points…
We revisit the problem of constructing predictive confidence sets for which we wish to obtain some type of conditional validity. We provide new arguments showing how ``split conformal'' methods achieve near desired coverage levels with high…
Probability theory is fundamental for modeling uncertainty, with traditional probabilities being real and non-negative. Complex probability extends this concept by allowing complex-valued probabilities, opening new avenues for analysis in…