\begin{equation}
H_0: \lambda_{\tau, (a)}^{0i}(x) = \lambda_{\tau, (a')}^{0i}(x),
\quad \text{v.s.} \quad
H_1: \lambda_{\tau, (a)}^{0i}(x) \neq \lambda_{\tau, (a')}^{0i}(x),
\label{eq:H0}
\end{equation}
