Related papers: Generalized Fr\'{e}chet means with random minimizi…
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The recently proposed generalized epidemic modeling framework (GEMF) \cite{sahneh2013generalized} lays the groundwork for systematically constructing a broad spectrum of stochastic spreading processes over complex networks. This article…
An interesting line of research is the investigation of the laws of random variables known as Dirichlet means. However, there is not much information on interrelationships between different Dirichlet means. Here, we introduce two…
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The mean field methods, which entail approximating intractable probability distributions variationally with distributions from a tractable family, enjoy high efficiency, guaranteed convergence, and provide lower bounds on the true…
Given a distribution $\rho$ on persistence diagrams and observations $X_1,...X_n \stackrel{iid}{\sim} \rho$ we introduce an algorithm in this paper that estimates a Fr\'echet mean from the set of diagrams $X_1,...X_n$. If the underlying…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…
A famous characterization theorem due to C.F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean for all samples of all sample sizes if and only if the family is Gaussian. There…
We in this paper consider Fr\'echet sufficient dimension reduction with responses being complex random objects in a metric space and high dimension Euclidean predictors. We propose a novel approach called weighted inverse regression…
In this paper, we introduce a new generalization of geometric distribution which can also viewed as discrete analogue of weighted exponential distribution introduced by Gupta and Kundu(2009). We study some basic distributional properties…
A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…
We establish finite-sample error bounds in expectation for transformed Fr\'echet means in Hadamard spaces under minimal assumptions. Transformed Fr\'echet means provide a unifying framework encompassing classical and robust notions of…