This paper deals with the existence issue of non-central Wishart distributions which is a research topic initiated by Wishart (1928), [10] and with important contributions by e.g., Lévy (1937) [7], Gindikin (1975) [4], Shanbhag (1988) [9], Peddada and Richards (1991) [8]. We present a new...

We introduce a new index to detect dependence in trivariate distributions. The index is based on the maximization of the coefficients of directional dependence over the set of directions. We show how to calculate the index using the three pairwise Spearman’s rho coefficients and the three...

Suppose we observe a Markov chain taking values in a functional space. We are interested in exploiting the time series dependence in these infinite dimensional data in order to make non-trivial predictions about the future. Making use of the Karhunen–Loève (KL) representation of functional...

The problem of test of fit for Vector AutoRegressive (VAR) processes with unconditionally heteroscedastic errors is studied. This problem is motivated by numerous examples of series presenting such a pattern. Our analysis is based on the residual autocorrelations obtained from Ordinary Least...

We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Lévy noises. We do not impose any moment condition on the driving Lévy process. Under certain regularity conditions on the drift function, we obtain consistency and rate of...

The paper categorizes discrete multivariate distributions into classes according to the forms of their probability generating functions, putting especial emphasis on those with pgf’s involving Lauricella functions. The LPSDs are Lauricella power series distributions where the arguments of the...

We consider penalized singular value decomposition (SVD) for a (noisy) data matrix when the left singular vector has a sparse structure and the right singular vector is a discretized function. Such situations typically arise from spatio-temporal data where only some small spatial regions are...

It is known (Hofmann-Credner and Stolz (2008) [4]) that the convergence of the mean empirical spectral distribution of a sample covariance matrix Wn=1/nYnYnt to the Marčenko–Pastur law remains unaffected if the rows and columns of Yn exhibit some dependence, where only the growth of the...

As one of the criteria for comparing variabilities among distributions, the sample range has attracted considerable attention in past decades. In this paper, we establish stochastic comparison results of sample ranges arising from two sets of heterogeneous exponential samples. It is shown that...

This work proposes a class of hierarchical models for geostatistical count data that includes the model proposed by Diggle et al. (1998)  [13] as a particular case. For this class of models the main second-order properties of the count variables are derived, and three models within this class...