On characterizing the complex Wishart distribution

In this research paper, we generalized the results of Ignacy in the multivariate case in order to characterize the complex Wishart distribution.

Structural breaks in cointegration models: Multivariate case

This review discusses methods of testing for a cointegration rank in a multivariate time series in the presence of structural breaks. The review covers both the methods with known and unknown break date. Multiple breaks are also considered. The issues of testing for cointegration with a possible change in the cointegration rank over time are discussed separately.

Approximative characteristics of the Nikol'skii-Besov-type classes of periodic functions in the space $B_{\infty,1}$

We obtained the exact order estimates of the orthowidths and similar to them approximative characteristics of the Nikol'skii-Besov-type classes $B^{\Omega}_{p,\theta}$ of periodic functions of one and several variables in the space $B_{\infty,1}$. We observe, that in the multivariate case $(d\geq2)$ the orders of orthowidths of the considered functional classes are realized by their approximations by step hyperbolic Fourier sums that contain the necessary number of harmonics. In the univariate case, an optimal in the sense of order estimates for orthowidths of the corresponding functional classes there are the ordinary partial sums of their Fourier series. Besides, we note that in the univariate case the estimates of the considered approximative characteristics do not depend on the parameter $\theta$. In addition, it is established that the norms of linear operators that realize the order of the best approximation of the classes $B^{\Omega}_{p,\theta}$ in the space $B_{\infty,1}$ in the multivariate case are unbounded.

Asymptotics of Bivariate Analytic Functions with Algebraic Singularities

International audience In this paper, we use the multivariate analytic techniques of Pemantle and Wilson to find asymptotic for- mulae for the coefficients of a broad class of multivariate generating functions with algebraic singularities. Flajolet and Odlyzko (1990) analyzed the coefficients of a class of univariate generating functions with algebraic singularities. These results have been extended to classes of multivariate generating functions by Gao and Richmond (1992) and Hwang (1996, 1998), in both cases by immediately reducing the multivariate case to the univariate case. Pemantle and Wilson (2013) outlined new multivariate analytic techniques and used them to analyze the coefficients of rational generating functions.