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

Abstract

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.

Keywords: Bilinear regression; Estimating equations; Flip- flop algorithm; Kronecker product structure; Linear structured covariance matrix; Maximum likelihood estimation.