Related papers: Fr\'echet Analysis Of Variance For Random Objects

We study a generalization of the Fr\'echet mean on metric spaces, which we call $\phi$-means. Our generalization is indexed by a convex function $\phi$. We find necessary and sufficient conditions for $\phi$-means to be finite and provide a…

We present a general M-estimation framework for inference on the wavelet variance. This framework generalizes the results on the scale-wise properties of the standard estimator and extends them to deliver the joint asymptotic properties of…

Since the seminal work by Beresteanu and Molinari(2008), the random set theory and related inference methods have been widely applied in partially identified econometric models. Meanwhile, there is an emerging field in statistics for…

When conducting a meta-analysis of standardized mean differences (SMDs), it is common to assume equal variances in the two arms of each study. This leads to Cohen's $d$ estimates for which interpretation is simple. However, this simplicity…

Barycenters (aka Fr\'echet means) were introduced in statistics in the 1940's and popularized in the fields of shape statistics and, later, in optimal transport and matrix analysis. They provide the most natural extension of linear…

We study the linear eigenvalue statistics of large random graphs in the regimes when the mean number of edges for each vertex tends to infinity. We prove that for a rather wide class of test functions the fluctuations of linear eigenvalue…

For sets $\mathcal Q$ and $\mathcal Y$, the generalized Fr\'echet mean $m \in \mathcal Q$ of a random variable $Y$, which has values in $\mathcal Y$, is any minimizer of $q\mapsto \mathbb E[\mathfrak c(q,Y)]$, where $\mathfrak c \colon…

This article develops nonparametric inference procedures for estimation and testing problems for means on manifolds. A central limit theorem for Frechet sample means is derived leading to an asymptotic distribution theory of intrinsic…

The infinite-dimensional Hilbert sphere $S^\infty$ has been widely employed to model density functions and shapes, extending the finite-dimensional counterpart. We consider the Fr\'echet mean as an intrinsic summary of the central tendency…

The sample median is often used in statistical analyses of physical or astronomical data wherein a central value must be found from samples polluted by elements which do not belong to the population of interest or when the underlying…

Let $(M,g)$ be a Riemannian manifold. If $\mu$ is a probability measure on $M$ given by a continuous density function, one would expect the Fr\'{e}chet means of data-samples $Q=(q_1,q_2,\dots, q_N)\in M^N$, with respect to $\mu$, to behave…

In applied research, Lee (2009) bounds are widely applied to bound the average treatment effect in the presence of selection bias. This paper extends the methodology of Lee bounds to accommodate outcomes in a general metric space, such as…

We introduce a location statistic for distributions on non-linear geometric spaces, the diffusion mean, serving as an extension and an alternative to the Fr\'echet mean. The diffusion mean arises as the generalization of Gaussian maximum…

We compute the Fr\'echet mean $\mathscr{E}_t$ of the solution $X_{t}$ to a continuous-time stochastic differential equation in a Lie group. It provides an estimator with minimal variance of $X_{t}$. We use it in the context of Kalman…

Variational inference is a general framework to obtain approximations to the posterior distribution in a Bayesian context. In essence, variational inference entails an optimization over a given family of probability distributions to choose…

The Central Limit Theorem provides a foundation for inferential statistics and hypothesis testing. It describes how standardized statistics behave under repeated sampling from large populations. However, if the size of the sample (n)…

This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently…

Random variables in metric spaces indexed by time and observed at equally spaced time points are receiving increased attention due to their broad applicability. The absence of inherent structure in metric spaces has resulted in a literature…

For a L\'evy basis $L$ on $\mathbb{R}^d$ and a suitable kernel function $f:\mathbb{R}^d \to \mathbb{R}$, consider the continuous spatial moving average field $X=(X_t)_{t\in \mathbb{R}^d}$ defined by $X_t = \int_{\mathbb{R}^d} f(t-s) \,…

In this letter we study the weak-convergence properties of random variables generated by unsharp quantum measurements. More precisely, for a sequence of random variables generated by repeated unsharp quantum measurements, we study the limit…