s p} + \mathbf{E}_{n \times p}\).
The usual least squares estimate of \(\boldsymbol{\beta}\) is given by
\(\mathbf{B} = (\mathbf{X}^{T} \mathbf{X})^{-1}  \mathbf{X}^{T} \mathbf{Y}\).</p>
<p>Then let</p><ul><li><p>\(\mathbf{X}_I\) be the submatrix of \(\mathbf{X}\) whose \(m\) rows are indexed by \(I\),</p></li>
<li><p>\(\mathbf{X}_{(-I)}\) is the complement, the submatrix of \(\mathbf{X}\) with the \(m\) rows in \(I\) deleted,</p></li>
</ul><p>Matrices \(\mathbf{Y}_I\), \(\mathbf{Y}_{(-I)}\) are defined sim