content_image/306456.jpg content_image/306457.jpg content_image/306458.jpg content_image/306459.jpg content_image/306460.jpg content_image/306462.jpg
Now we need the formula (Henderson and Searle, 1981) 

which implies 

<img src='content_image/306456.jpg'>

<img src='content_image/306457.jpg'>

Note that to use this block matrix inversion formula we require B$_{T}$$_{l}$$_{+1}$$_{T}$$_{l}$$_{+1}$A − 1 T$_{l}$$_{T$_{l}$}$+ I$_{|}$$_{T}$$_{l}$$_{|}$ to be invertible. However, by the previous result of this theorem only the variance of the intercept term in the form for A − 1 T$_{l}$T$_{l}$ is dependent upon the value of t , so we have that 

<img src='content_image/306458.jpg'>

for some V$_{1}$, V$_{2}$ ; dim( V$_{1}$ ) = 1 × 1 , dim( V$_{2}$ ) = | W$_{l}$ | × 1. Now, by Lemma 4.4 det( B − 1 T$_{l}$$_{+1}$$_{T$_{l}$$_{+1}$}$) > 0, which gives det( B$_{T}$$_{l}$$_{+1}$$_{T}$$_{l}$$_{+1}$ ) = { det( B − 1 T$_{l}$$_{+1}$$_{T$_{l}$$_{+1}$}$) } − 1 > 0. By assumption det( A − 1 T$_{l}$$_{T$_{l}$}$) > 0, and thus 

Therefore 

and B$_{T}$$_{l}$$_{+1}$$_{T}$$_{l}$$_{+1}$A − 1 T$_{l}$T$_{l}$ + I$_{|}$$_{T}$$_{l}$$_{|}$ is therefore invertible as required. Now 

<img src='content_image/306459.jpg'>

<img src='content_image/306460.jpg'>

<img src='content_image/306462.jpg'>

