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A consistent estimator for spectral density matrix of a discrete time periodically correlated process

Azimmohseni M., Soltani A. R., Khalafi M., Ghalesary N. M.

Probability and Mathematical Statistics

2018

Vol. 38, Fasc. 1

225--242

In this article, we introduce a weighted periodogram in the class of smoothed periodograms as a consistent estimator for the spectra density matrix of a periodically correlated process. We derive its li miting distribution that appears to be a certain finite linear combination of Wishart distribution. We also provide numerical derivations for our smoothed period ogram and exhibit its asymptotic consistency using simulated data.

The Fisher information and exponential families parametrized by a segment of means

Graczyk P., Mamane S.

Probability and Mathematical Statistics

2015

Vol. 35, Fasc. 1

73--90

We consider natural and general exponential families (Qm)mϵM on Rd parametrized by the means. We study the submodels (Q0m1+(1−0)m2)0ϵ[0, 1] parametrized by a segment in the means domain from the point of view of the Fisher information. Such a parametrization allows for a parsimonious model and is particularly useful in practical situations when hesitating between two parameters m1 and m2. The most interesting cases are multivariate Gaussian and Wishart models with matrix parameters.

Probability on matrix-cone hypergroups: limit theorems and structural properties

Hazod W.

Journal of Applied Analysis

2009

Vol. 15, nr 2

205-245

Recent investigations of M. Rösler [13] and M. Voit [17] provide examples of hypergroups with properties similar to the group-or vector space case and with a sufficiently rich structure of automorphisms, providing thus tools to investigate the limit theory of normalized random walks and the structure of the corresponding limit, laws. The investigations are parallel to corresponding investigations for vector spaces and simply connected nilpotent Lie groups.