Related papers: Total positivity in exponential families with appl…
This paper considers an extension of the multivariate symmetric Laplace distribution to matrix variate case. The symmetric Laplace distribution is a scale mixture of normal distribution. The maximum likelihood estimators (MLE) of the…
The $p$-tensor Ising model is a one-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic is a multi-linear form of degree $p \geq 2$. This is a natural generalization of the matrix Ising…
Lately, a New Transmuted Logistic-exponential (NTLE) distribution was introduced and studied as an extension of the Logistic-Exponential Distribution (LED) with wider applicability in lifetime modelling. However, the maximum likelihood…
While standard estimation assumes that all datapoints are from probability distribution of the same fixed parameters $\theta$, we will focus on maximum likelihood (ML) adaptive estimation for nonstationary time series: separately estimating…
Maximum likelihood estimation (MLE) is a fundamental problem in statistics. Characteristics of the MLE problem for discrete algebraic statistical models are reflected in the geometry of the $\textit{likelihood correspondence}$, a variety…
The exponential-family random graph models (ERGMs) have emerged as an important framework for modeling social networks for a wide variety of relational types. ERGMs for valued networks are less well-developed than their unvalued…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
The article is devoted to the study of exponential statistical structures of type B, which constitute a subclass of exponential families of probability distributions. This class is characterized by a number of analytical and probabilistic…
In this paper, we derive closed-form estimators for the parameters of certain exponential family distributions through the maximum a posteriori (MAP) equations. A Monte Carlo simulation is conducted to assess the performance of the proposed…
We give a useful new characterization of the set of all completely positive, trace-preserving (i.e., stochastic) maps from 2x2 matrices to 2x2 matrices. These conditions allow one to easily check any trace-preserving map for complete…
Multiplicativity of certain maximal p -> q norms of a tensor product of linear maps on matrix algebras is proved in situations in which the condition of complete positivity (CP) is either augmented by, or replaced by, the requirement that…
The asymptotic normality of the Maximum Likelihood Estimator (MLE) is a cornerstone of statistical theory. In the present paper, we provide sharp explicit upper bounds on Zolotarev-type distances between the exact, unknown distribution of…
Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling to learn latent representations in modern multivariate data sets with complex dependency structures. Among…
This paper investigates the asymptotic distribution of the maximum-likelihood estimate (MLE) in multinomial logistic models in the high-dimensional regime where dimension and sample size are of the same order. While classical large-sample…
We study the distribution of the maximum likelihood estimate (MLE) in high-dimensional logistic models, extending the recent results from Sur (2019) to the case where the Gaussian covariates may have an arbitrary covariance structure. We…
Let G = An be the graph corresponding to the graphical model of nearest neighbour interaction in a Gaussian character. We study Natural Exponential Families( NEF) ofWishart distributions on convex cones QG and PG, where PG is the cone of…
This paper investigates maximizers of the information divergence from an exponential family $E$. It is shown that the $rI$-projection of a maximizer $P$ to $E$ is a convex combination of $P$ and a probability measure $P_-$ with disjoint…
We provide a polyhedral description of the conditions for the existence of the maximum likelihood estimate (MLE) for a hierarchical log-linear model. The MLE exists if and only if the observed margins lie in the relative interior of the…
We study the problem of episodic reinforcement learning in continuous state-action spaces with unknown rewards and transitions. Specifically, we consider the setting where the rewards and transitions are modeled using parametric bilinear…
Nonparametric tests for equality of multivariate distributions are frequently desired in research. It is commonly required that test-procedures based on relatively small samples of vectors accurately control the corresponding Type I Error…