Afrika Statistika

Bilinear regression model with Kronecker and linear structures for the covariance matrix

Joseph NZABANIT, Dietrich VON ROSEN, and Martin SINGULL

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In this paper, the bilinear regression model based on normally distributed random matrix is studied. For these models, the dispersion matrix has the so called Kronecker product structure and they can be used for example to model data with spatio-temporal relationships. The aim is to estimate the parameters of the model when, in addition, one covariance matrix is assumed to be linearly structured. On the basis of n independent observations from a matrix normal distribution, estimating equations in a flip-flop relation are established and the consistency of estimators is studied.


Nous abordons dans ce papier du model de regression bilinéaire basé sur une matrice aléatoire gaussienne. Dans les modèles que nous étudions, les matrices de dispersion ont la structure du produit de Kronecker si bien qu'elles sont capables de modéliser les données présentant des relations spatio-temporelles. Le but de cette étude est d'estimer les paramètres du modèle, lorsqu'en plus une matrice de covariance est supposée être linéairement structurée. Etant données n observations normalement distribuées, les équations d'estimation sont établies à travers une relation flip-flop. La consistence des estimateurs est étudiée.

Article information

Afr. Stat., Volume 10, Number 2 (2015), 827- 837.

First available in Project Euclid: 19 February 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression 62J05

Bilinear regression estimating equations flip-flop algorithm Kronecker product structure linear structured covariance matrix aximum likelihood estimation


NZABANIT, Joseph; VON ROSEN, Dietrich; SINGULL, Martin. Bilinear regression model with Kronecker and linear structures for the covariance matrix. Afr. Stat. 10 (2015), no. 2, 827-- 837. doi:10.1010/sample.1010101010.

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