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$\displaystyle {({\bf Y} - {\bf X}\hat{\boldsymbol{\beta}})'
\left\{{\bf X}({\bf...
...}
\right]^{-1}(\boldsymbol{\theta} - {\bf C}\hat{\boldsymbol{\beta}})
\right\}}$
  $\displaystyle =$ $\displaystyle ({\bf Y} - {\bf X}\hat{\boldsymbol{\beta}})'
\left\{ {\bf X}({\bf...
... C}({\bf X}'{\bf X})^{-1}{\bf C}']^{-1}{\bf C}\hat{\boldsymbol{\beta}} \right\}$  
  $\displaystyle =$ $\displaystyle {\bf Y}'{\bf X}({\bf X}'{\bf X})^{-1}{\bf C}'[{\bf C}({\bf X}'{\b...
... C}'[{\bf C}({\bf X}'{\bf X})^{-1}{\bf C}']^{-1}{\bf C}\hat{\boldsymbol{\beta}}$  
    $\displaystyle - \hat{\boldsymbol{\beta}}'{\bf X}'{\bf X} ({\bf X}'{\bf X})^{-1}...
... C}'[{\bf C}({\bf X}'{\bf X})^{-1}{\bf C}']^{-1}{\bf C}\hat{\boldsymbol{\beta}}$  
  $\displaystyle =$ $\displaystyle \hat{\boldsymbol{\beta}}'{\bf C}'[{\bf C}({\bf X}'{\bf X})^{-1}{\...
... C}'[{\bf C}({\bf X}'{\bf X})^{-1}{\bf C}']^{-1}{\bf C}\hat{\boldsymbol{\beta}}$  
    $\displaystyle - \hat{\boldsymbol{\beta}}' {\bf C}'[{\bf C}({\bf X}'{\bf X})^{-1...
... C}'[{\bf C}({\bf X}'{\bf X})^{-1}{\bf C}']^{-1}{\bf C}\hat{\boldsymbol{\beta}}$  
  $\displaystyle =$ 0  



Frank Starmer 2004-05-19
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