Related papers: Asymptotic Matrix Variate von-Mises Fisher and Bin…
One of the major problems for maximum likelihood estimation in the well-established directional models is that the normalising constants can be difficult to evaluate. A new general method of "score matching estimation" is presented here on…
Orthonormal matrices play an important role in reduced-rank matrix approximations and the analysis of matrix-valued data. A matrix Bingham-von Mises-Fisher distribution is a probability distribution on the set of orthonormal matrices that…
A large class of modern probabilistic learning systems assumes symmetric distributions, however, real-world data tend to obey skewed distributions and are thus not always adequately modelled through symmetric distributions. To address this…
We illustrate the use of the R-package "rstiefel" for matrix-variate data analysis in the context of two examples. The first example considers estimation of a reduced-rank mean matrix in the presence of normally distributed noise. The…
For positive integers $d$ and $p$ such that $d \ge p$, let $\mathbb{R}^{d \times p}$ denote the set of $d \times p$ real matrices, $I_p$ be the identity matrix of order $p$, and $V_{d,p} = \{x \in \mathbb{R}^{d \times p} \mid x'x = I_p\}$…
In many statistical signal processing applications, the estimation of nuisance parameters and parameters of interest is strongly linked to the resulting performance. Generally, these applications deal with complex data. This paper focuses…
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
The noncentral Wishart distribution has become more mainstream in statistics as the prevalence of applications involving sample covariances with underlying multivariate Gaussian populations as dramatically increased since the advent of…
When observations are truncated, we are limited to an incomplete picture of our dataset. Recent methods propose to use score matching for truncated density estimation, where the access to the intractable normalising constant is not…
We study properties of Fisher distribution (von Mises-Fisher distribution, matrix Langevin distribution) on the rotation group SO(3). In particular we apply the holonomic gradient descent, introduced by Nakayama et al. (2011), and a method…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
This paper considers statistical estimation problems where the probability distribution of the observed random variable is invariant with respect to actions of a finite topological group. It is shown that any such distribution must satisfy…
This study presents a new procedure for necessary tests of multivariate normality based on the uniform distribution on the Stiefel manifold. We demonstrate that the test statistic, which is formed by the product of the scaled residual…
We discuss generalized linear models for directional data where the conditional distribution of the response is a von Mises-Fisher distribution in arbitrary dimension or a Bingham distribution on the unit circle. To do this properly, we…
Random orthogonal matrices play an important role in probability and statistics, arising in multivariate analysis, directional statistics, and models of physical systems, among other areas. Calculations involving random orthogonal matrices…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop…
Generalized likelihoods are commonly used to obtain consistent estimators with attractive computational and robustness properties. Formally, any generalized likelihood can be used to define a generalized posterior distribution, but an…
Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…