\widehat\mathbf{\Omega}_n &= \bigg(\frac{1}{n} \sum_i \mathbf{x}_i \mathbf{x}_i^{\top} \bigg)^{-1} \bigg(\frac{1}{n} \sum_i \mathbf{x}_i \mathbf{x}_i^{\top} \widehat \varepsilon_i^2 \bigg) \bigg(\frac{1}{n} \sum_i \mathbf{x}_i \mathbf{x}_i^{\top} \bigg)^{-1} \\
