Related papers: A Matrix Variate Skew-t Distribution
Considering discrete models, the univariate framework has been studied in depth compared to the multivariate one. This paper first proposes two criteria to define a sensu stricto multivariate discrete distribution. It then introduces the…
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance…
In the past few years, there have been a number of proposals for generalizing the factor analysis (FA) model and its mixture version (known as mixtures of factor analyzers (MFA)) using non-normal and asymmetric distributions. These models…
This paper addresses the path-planning challenge for very large-scale robotic systems (VLSR) operating in complex and cluttered environments. VLSR systems consist of numerous cooperative agents or robots working together autonomously.…
Matrix sketching is a powerful tool for reducing the size of large data matrices. Yet there are fundamental limitations to this size reduction when we want to recover an accurate estimator for a task such as least square regression. We show…
A new family of multivariate distributions, which shall be termed multivector variate distributions, based in the family of the multivariate contoured elliptically distribution is proposed. Several particular cases of multivector variate…
Skew normal mixture models provide a more flexible framework than the popular normal mixtures for modelling heterogeneous data with asymmetric behaviors. Due to the unboundedness of likelihood function and the divergency of shape…
Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by…
Multivariate extreme value distributions are a common choice for modelling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate max-stable…
The gamma distribution is a useful model for small area prediction of a skewed response variable. We study the use of the gamma distribution for small area prediction. We emphasize a model, called the gamma-gamma model, in which the area…
We introduce a new multivariate circular linear distribution suitable for modeling direction and speed in (multiple) animal movement data. To properly account for specific data features, such as heterogeneity and time dependence, a hidden…
The joint distribution of two off-diagonal Wishart matrix elements was useful in recent work on geometric probability [Finch 2010]. Not finding such formulas in the literature, we report these here.
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
In the mixture models problem it is assumed that there are $K$ distributions $\theta_{1},\ldots,\theta_{K}$ and one gets to observe a sample from a mixture of these distributions with unknown coefficients. The goal is to associate instances…
We examine the problem of computing multivariate scenarios sets for skewed distributions. Our interest is motivated by the potential use of such sets in the "stress testing" of insurance companies and banks whose solvency is dependent on…
Stochastic variance reduced methods have gained a lot of interest recently for empirical risk minimization due to its appealing run time complexity. When the data size is large and disjointly stored on different machines, it becomes…
The t-distribution has many useful applications in robust statistical analysis. The parameter estimation of the t-distribution is carried out using ML estimation method, and the ML estimates are obtained via the EM algorithm. In this study,…
Upper bounds are derived on the total variation distance between the invariant distributions of two stochastic matrices differing on a subset W of rows. Such bounds depend on three parameters: the mixing time and the minimal expected…
Models based on multivariate t distributions are widely applied to analyze data with heavy tails. However, all the marginal distributions of the multivariate t distributions are restricted to have the same degrees of freedom, making these…
Statistical models for multivariate data often include a semi-orthogonal matrix parameter. In many applications, there is reason to expect that the semi-orthogonal matrix parameter satisfies a structural assumption such as sparsity or…