Related papers: The Stein Effect for Frechet Means
A new class of minimax Stein-type shrinkage estimators of a multivariate normal mean is studied where the shrinkage factor is based on an l_p norm. The proposed estimators allow some but not all coordinates to be estimated by 0 thereby…
Statistical analysis is increasingly confronted with complex data from metric spaces. Petersen and M\"uller (2019) established a general paradigm of Fr\'echet regression with complex metric space valued responses and Euclidean predictors.…
In the geosciences, a recurring problem is one of estimating spatial means of a physical field using weighted averages of point observations. An important variant is when individual observations are counted with some probability less than…
This note shows how to apply the James-Stein estimator to the case of entropic uncertainty relations of more than two observables. A better result is found compared to applying the ordinary estimator and we find a more optimal model…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
The problem of estimating a normal covariance matrix is considered from a decision-theoretic point of view, where the dimension of the covariance matrix is larger than the sample size. This paper addresses not only the nonsingular case but…
We derive a new discrepancy statistic for measuring differences between two probability distributions based on combining Stein's identity with the reproducing kernel Hilbert space theory. We apply our result to test how well a probabilistic…
A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…
The problem of estimating a mean matrix of a multivariate complex normal distribution with an unknown covariance matrix is considered under an invariant loss function. By using complex versions of the Stein identity, the Stein-Haff…
In the past decades, the central limit theorem (CLT) has been generalized to non-Euclidean data spaces. Some years ago, it was found that for some random variables on the circle, the sample Fr\'echet mean fluctuates around the population…
We consider quasi-admissibility/inadmissibility of Stein-type shrinkage estimators of the mean of a multivariate normal distribution with covariance matrix an unknown multiple of the identity. Quasi-admissibility/inadmissibility is defined…
This paper considers the problem of estimating a high-dimensional vector of parameters $\boldsymbol{\theta} \in \mathbb{R}^n$ from a noisy observation. The noise vector is i.i.d. Gaussian with known variance. For a squared-error loss…
We consider two statistical problems at the intersection of functional and non-Euclidean data analysis: the determination of a Fr\'echet mean in the Wasserstein space of multivariate distributions; and the optimal registration of deformed…
The space of positive definite symmetric matrices has been studied extensively as a means of understanding dependence in multivariate data along with the accompanying problems in statistical inference. Many books and papers have been…
Samples with a common mean but possibly different, ordered variances arise in various fields such as interlaboratory experiments, field studies or the analysis of sensor data. Estimators for the common mean under ordered variances typically…
Many spatial models exhibit locality structures that effectively reduce their intrinsic dimensionality, enabling efficient approximation and sampling of high-dimensional distributions. However, existing approximation techniques primarily…
Random objects are complex non-Euclidean data taking value in general metric space, possibly devoid of any underlying vector space structure. Such data are getting increasingly abundant with the rapid advancement in technology. Examples…
We propose a novel test for assessing partial effects in Frechet regression on Bures Wasserstein manifolds. Our approach employs a sample splitting strategy: the first subsample is used to fit the Frechet regression model, yielding…
An unbiased estimator for the ellipticity of an object in a noisy image is given in terms of the image moments. Three assumptions are made: i) the pixel noise is normally distributed, although with arbitrary covariance matrix, ii) the image…
Existing concentration bounds for bounded vector-valued random variables include extensions of the scalar Hoeffding and Bernstein inequalities. While the latter is typically tighter, it requires knowing a bound on the variance of the random…