span> represent the <span class="arithmatex">\(j\)</span>-th column in <span class="arithmatex">\(\bb{X}_j\)</span> and <span class="arithmatex">\(\bb{X}\)</span>, respectively. That is, <span class="arithmatex">\(x_j^\ast\)</span> is a permutation of <span class="arithmatex">\(x_j\)</span>. </p>
<p>We need to assume that <span class="arithmatex">\(\bb{X}^T\bb{X}=\bb{I}.\)</span> It's easy to see that <span class="arithmatex">\(E_p[x_j^\ast] = \bar x_j=\bb{0}\)</span>, which is a zero-vector. Also, by defin