GLS estimator of beta

[bx029297]

Hi guys,

I know how to derive the GLS estimator of beta (theoretical GLS), but there a slight change to the question and i am not quite sure how to go about it.

A researcher has reason to believe that the disturbances in the standard model are heteroscedastic, with a threefold block-diagonal structure, such that:

Y1= X1\beta + U1

Y2= X2\beta + U2

Y3= X3\beta + U3

where Yi is Ti x 1,

Xi is Ti x k matrix of regressors,

Ui is a Ti x 1 vector of disturbances and

\beta is a k x 1vector of population regression coefficients assumed to be the same for each of the blocks.

Assume that the only departure from the standard assumptions is that:

E(UiUi')= \sigma^{2}_{i}ITi

where is the identity matrix of order .

My question is simply how to obtain the GLS estimator of \beta assuming that the \sigma^{2}_{i} are known.

any hints?

regards