Prove that under the hypothesis of normality for every fixed integer \(d \geq 1\),
1. \(E\left[\widehat{\mathcal{E}}_{n, d}ight]\) is bounded above by a finite constant that depends only on \(d\).

2. For every fixed \(\alpha \in(0,1)\), the sequence of critical values \(c_{\alpha, n, d}\) of \(\widehat{\mathcal{E}}_{n, d}\) are bounded above by a finite constant \(k_{\alpha, d}\) that depends only on \(\alpha\) and \(d\).