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We study a well-known problem concerning a random variable $Z$ uniformly distributed between two independent random variables. A new extension has been introduced for this problem and fairly large classes of randomly weighted average…

This paper focuses on the estimation of the sample covariance matrix from low-dimensional random projections of data known as compressive measurements. In particular, we present an unbiased estimator to extract the covariance structure from…

This paper proposes factor stochastic volatility models with skew error distributions. The generalized hyperbolic skew t-distribution is employed for common-factor processes and idiosyncratic shocks. Using a Bayesian sparsity modeling…

Context: Statistical properties of the cosmic density fields are to a large extent encoded in the shape of the one-point density probability distribution functions (PDF). In order to successfully exploit such observables, a detailed…

We extend the well-known $\beta$-model for directed graphs to dynamic network setting, where we observe snapshots of adjacency matrices at different time points. We propose a kernel-smoothed likelihood approach for estimating $2n$…

The skew-normal and related families are flexible and asymmetric parametric models suitable for modelling a diverse range of systems. We show that the multivariate maximum of a high-dimensional extended skew-normal random sample has…

In the this paper, the authors propose to estimate the density of a targeted population with a weighted kernel density estimator (wKDE) based on a weighted sample. Bandwidth selection for wKDE is discussed. Three mean integrated squared…

Matrix normal models have an associated 4-tensor for their covariance representation. The covariance array associated with a matrix normal model is naturally represented as a Kronecker-product structured covariance associated with the…

We consider the empirical eigenvalue distribution of random real symmetric matrices with stochastically independent skew-diagonals and study its limit if the matrix size tends to infinity. We allow correlations between entries on the same…

Dense retrieval models use bi-encoder network architectures for learning query and document representations. These representations are often in the form of a vector representation and their similarities are often computed using the dot…

This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…

We study the kernel estimator of the transition density of bifurcating Markov chains. Under some ergodic and regularity properties, we prove that this estimator is consistent and asymptotically normal. Next, in the numerical studies, we…

We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. We show that this definition extends a recent construction of Schubert polynomials due to Bergeron…

Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B…

When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…

This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The…

This papers presents a generalization of the Weitzman overlapping coefficient, originally defined for two probability density functions, to a setting involving k independent distributions, denoted by Delta. To estimate this generalized…

We introduce a new ensemble of random bipartite graphs, which we term the `smearing ensemble', where each left node is connected to some number of consecutive right nodes. Such graphs arise naturally in the recovery of sparse wavelet…

Recently, random graphs in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices have attracted much attention. Here, we present a specific realization of a class of random…

We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…