Related papers: Improved parameter estimation for a family of expo…
Since its introduction, the skew-$t$ distribution has received much attention in the literature both for the study of theoretical properties and as a model for data fitting in empirical work. A major motivation for this interest is the high…
For integer valued random variables, the translated Poisson distributions form a flexible family for approximation in total variation, in much the same way that the normal family is used for approximation in Kolmogorov distance. Using the…
This paper considers the problem of robustly estimating the parameters of a heavy-tailed multivariate distribution when the covariance matrix is known to have the structure of a low-rank matrix plus a diagonal matrix as considered in factor…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
The classic Hettmansperger-Randles Estimator has found extensive use in robust statistical inference. However, it cannot be directly applied to high-dimensional data. In this paper, we propose a high-dimensional Hettmansperger-Randles…
We present an algorithmic approach to estimate the value distributions of random variables of probabilistic loops whose statistical moments are (partially) known. Based on these moments, we apply two statistical methods, Maximum Entropy and…
We consider discrete graphical models Markov with respect to a graph $G$ and propose two distributed marginal methods to estimate the maximum likelihood estimate of the canonical parameter of the model. Both methods are based on a…
The Sherrington--Kirkpatrick model of spin glasses, the Hopfield model of neural networks and the Ising spin glass are all models of binary data belonging to the one-parameter exponential family with quadratic sufficient statistic. Under…
The main approach to inference for multivariate extremes consists in approximating the joint upper tail of the observations by a parametric family arising in the limit for extreme events. The latter may be expressed in terms of…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
Marshall and Olkin (1997, Biometrika, 84, 641 - 652) introduced a very powerful method to introduce an additional parameter to a class of continuous distribution functions and hence it brings more flexibility to the model. They have…
A fundamental problem in statistics is estimating the shape matrix of an Elliptical distribution. This generalizes the familiar problem of Gaussian covariance estimation, for which the sample covariance achieves optimal estimation error.…
The class of $\alpha$-stable distributions is widely used in various applications, especially for modelling heavy-tailed data. Although the $\alpha$-stable distributions have been used in practice for many years, new methods for…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…
We investigate the problem of jointly testing a pair of composite hypotheses and, depending on the test result, estimating a random parameter under distributional uncertainties. Specifically, it is assumed that the distribution of the data…
We consider the problem of estimating the error variance in a general linear model when the error distribution is assumed to be spherically symmetric, but not necessary Gaussian. In particular we study the case of a scale mixture of…
We propose estimators for the parameters of the Linnik L$(\alpha,\gamma)$ distribution. The estimators are derived from the moments of the log-transformed Linnik distributed random variable, and are shown to be asymptotically unbiased. The…
In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…