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Nonparametric identification and maximum likelihood estimation for finite-state hidden Markov models are investigated. We obtain identification of the parameters as well as the order of the Markov chain if the transition probability…
We equip the polytope of $n\times n$ Markov matrices with the normalized trace of the Lebesgue measure of $\mathbb{R}^{n^2}$. This probability space provides random Markov matrices, with i.i.d. rows following the Dirichlet distribution of…
It is realized that existing powerful tests of goodness-of-fit are all based on sorted uniforms and, consequently, can suffer from the confounded effect of different locations and various signal frequencies in the deviations of the…
In a smooth semi-parametric model, the marginal posterior distribution for a finite dimensional parameter of interest is expected to be asymptotically equivalent to the sampling distribution of any efficient point-estimator. The assertion…
A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is general enough to encompass a number of…
We develop a geometric mechanism to prove the existence of orbits that drift along a prescribed sequence of cylinders, under some general conditions on the dynamics. This mechanism can be used to prove the existence of Arnold diffusion for…
Azzalini (1985) introduced a skew-normal distribution of which normal distribution is a special case. Recently Kundu (2014) introduced a geometric skew-normal distribution and showed that it has certain advantages over Azzalini's…
In competing risks models, the joint distribution of the event times is not identifiable even when the margins are fully known, which has been referred to as the "identifiability crisis in competing risks analysis" (Crowder, 1991). We model…
We consider random Hermitian matrices with independent upper triangular entries. Wigner's semicircle law says that under certain additional assumptions, the empirical spectral distribution converges to the semicircle distribution. We…
The Weibull function is widely used to describe skew distributions observed in nature. However, the origin of this ubiquity is not always obvious to explain. In the present paper, we consider the well-known Galton-Watson branching process…
Many real objects are modeled as discrete sets of points, such as corners or other salient features. For our main applications in chemistry, points represent atomic centers in a molecule or a solid material. We study the problem of…
Given a random sample of observations, mixtures of normal densities are often used to estimate the unknown continuous distribution from which the data come. Here we propose the use of this semiparametric framework for testing symmetry about…
We consider wave propagation in a complex structure coupled to a finite number $N$ of scattering channels, such as chaotic cavities or quantum dots with external leads. Temporal aspects of the scattering process are analysed through the…
This paper develops a density deconvolution estimator that assumes the density of interest is a member of the generalized skew-symmetric (GSS) family of distributions. Estimation occurs in two parts: a skewing function, as well as location…
The shortcomings of the traditional univariate distributions in the past greatly encouraged mathematical statisticians to develop new generalizations of distributions. The New Generalized Fisk distribution, a unique distribution presented…
We show that the Riemannian Gaussian distributions on symmetric spaces, introduced in recent years, are of standard random matrix type. We exploit this to compute analytically marginals of the probability density functions. This can be done…
Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…
It is well known that the ratio of two independent standard Gaussian random variables follows a Cauchy distribution. Any convex combination of independent standard Cauchy random variables also follows a Cauchy distribution. In a recent…
Pattern recognition constitutes a particularly important task underlying a great deal of scientific and technologica activities. At the same time, pattern recognition involves several challenges, including the choice of features to…
We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…