In this paper we consider the distribution of the product of a Wishart random matrix and a Gaussian random vector. We derive a stochastic representation for the elements of the product. Using this result, the exact joint density for an arbitrary linear combination of the elements of the product...

A methodology which allows applying the standard monitoring techniques for the mean behaviour of Gaussian processes in the detection of shifts in the covariance matrix is developed. Moreover, the proposed methodology allows the use of an estimator of the covariance matrix based on a single...

In this paper we discuss the distributions and independency properties of several generalizations of the Wishart distribution. First, an analog to Muirhead [R.J. Muirhead, Aspects of Multivariate Statistical Theory, Wiley, New York, 1982] Theorem 3.2.10 for the partitioned matrix is...

Abstract In this paper we consider the portfolio weights obtained by maximizing the expected quadratic utility function. The unknown parameters of the return process, the mean vector and the covariance matrix, are estimated by their sample counterparts. Assuming independent and multivariate...

Abstract In this paper, we consider the sample estimators for the expected return, the variance, the value-at-risk (VaR), and the conditional VaR (CVaR) of the minimum VaR and the minimum CVaR portfolio. Their exact distributions are derived. These expressions are used for studying the...

In this paper we derive the asymptotic distributions of the estimated weights and of estimated performance measures of the minimum value-at-risk portfolio and of the minimum conditional value-at-risk portfolio assuming that the asset returns follow a strictly stationary process. It is proved...

We estimate the global minimum variance (GMV) portfolio in the high-dimensional case using results from random matrix theory. This approach leads to a shrinkage-type estimator which is distribution-free and it is optimal in the sense of minimizing the out-of-sample variance. Its asymptotic...

In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that $p/n\rightarrow c\in (0, +\infty)$. The precision matrix is...

In this paper, we derive an exact test for a column of the covariance matrix. The test statistic is calculated by using a single observation. The exact distributions of the test statistic are derived under both the null and alternative hypotheses. We also obtain an analytical expression of the...