The distribution of Hermitian quadratic forms in elliptically contoured random vectors

Provost, Serge B.; Cheong, Young-Ho

doi:10.1016/s0378-3758(01)00096-9

Cited by 13 publications

(5 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An important issue is raised when considering Theorem 1.1, which is the mixture representation given by Equation (2) and the form of the weighting function w(·). Note that w(·) is not always nonnegative (see examples in Chu, [25] Provost and Cheong [26] and Arashi et al [27]). This makes a difference with respect to that of the class of multivariate scale mixtures of normal distributions.…”

Section: Discussionmentioning

confidence: 99%

Bayesian analysis in multivariate regression models with conjugate priors

et al. 2013

View full text Add to dashboard Cite

show abstract

Section: Discussionmentioning

confidence: 99%

Bayesian analysis in multivariate regression models with conjugate priors

et al. 2013

View full text Add to dashboard Cite

show abstract

“…Chu (1973) and Gupta and Varga (1995) demonstrates that real elliptical distributions can always be expanded as an integral of a set of normal pdfs. We report the result by Provost and Cheong (2002) as a useful lemma, defining the complex matrix variate elliptical distribution as a weighted representation of complex matrix variate normal pdfs. This representation can be used to explore the distribution of S when the distribution of X can be that of any member of the complex matrix variate elliptical class.…”

Section: Complex Noncentral Wishart Typementioning

confidence: 99%

A unified complex noncentral Wishart type distribution inspired by massive MIMO systems

Ferreira

Bekker

2019

J Stat Distrib App

View full text Add to dashboard Cite

The eigenvalue distributions from a complex noncentral Wishart matrix S = X H X has been the subject of interest in various real world applications, where X is assumed to be complex matrix variate normally distributed with nonzero mean M and covariance. This paper focuses on a weighted analytical representation of S to alleviate the restriction of normality; thereby allowing the choice of X to be complex matrix variate elliptically distributed for the practitioner. New results for eigenvalue distributions of more generalised forms are derived under this elliptical assumption, and investigated for certain members of the complex elliptical class. The distribution of the minimum eigenvalue enjoys particular attention. This theoretical investigation has proposed impact in communications systems (where massive datasets can be conveniently formulated in matrix terms), in particular the case where the noncentral matrix has rank one which is useful in practice.

show abstract

“…is a weighting function. We refer to Provost and Cheong (2002), Nkurunziza (2013) and Nkurunziza and Chen (2013) for more details and applications. Under our assumptions, the generalized least squares (GLS) estimator of β is of the formβ = (…”

Section: Model and Estimatorsmentioning

confidence: 99%

Shrinkage Estimation in Restricted Elliptical Regression Model

Falah

Arashi

Tabatabaey

2018

JIRSS

View full text Add to dashboard Cite

Abstract. In the restricted elliptical linear model, an approximation for the risk of a general shrinkage estimator of the regression vector-parameter is given. Superiority condition of the shrinkage estimator over the restricted estimator is investigated under the elliptical assumption. It is evident from numerical results that the shrinkage estimator performs better than the unrestricted one in the multivariate t-regression model.

show abstract

The distribution of Hermitian quadratic forms in elliptically contoured random vectors

Cited by 13 publications

References 21 publications

Bayesian analysis in multivariate regression models with conjugate priors

Bayesian analysis in multivariate regression models with conjugate priors

A unified complex noncentral Wishart type distribution inspired by massive MIMO systems

Shrinkage Estimation in Restricted Elliptical Regression Model

Contact Info

Product

Resources

About