In the proposed article, random matrices whose distribution coincides with the Wishart distribution are considered.Their elements, which are dependent, are represented as algebraic functions of independent random variables.The densities of the independent random variables are also indicated.A Wishart matrix construction is thus obtained.The present paper shows the relationship between the proposed Wishart matrix construction and correlations and partial correlations.The considered construction was also used to obtain a factorization of the determinant of a correlation matrix.
The purpose of this article is to introdused the inference techniques for the mean vector μ, the correlation matrix π and the covariance matrix Σ of the multivariate normal sample and to apply these techniques using the software package STATISTICA 13.0 (StatSoft Inc, USA). The sample contains 50 weekly return observations (in percent) on each of ten stock portfolios constructed from stocks on the Toronto Stock Exchanges. Since the data are obtained as a random sample of multivariate normal distribution the Wishart distribution can be used to make inference about covariance matrix.
