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\begin{aligned} y_{t} = X_{t}^{'} β + u_{t} : & {\hat{L M}}_{0} \overset{D}{⟶} \int_{0}^{1} Q_{1}^{2} (r) d r \\ y_{t} = μ + X_{t}^{'} β + u_{t} : & {\hat{L M}}_{μ} \overset{D}{⟶} \int_{0}^{1} Q_{2}^{2} (r) d r \\ y_{t} = μ + δ t + X_{t}^{'} β + u_{t} : & {\hat{L M}}_{τ} \overset{D}{⟶} \int_{0}^{1} Q_{3}^{2} (r) d r \end{aligned}

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\begin{align*} y_ t=X_ t'\beta + u_ t:\qquad & \widehat{\mi{LM}}_0\stackrel{D}{\longrightarrow }\int _0^1Q_1^2(r)dr\\ y_ t=\mu +X_ t'\beta + u_ t:\qquad & \widehat{\mi{LM}}_\mu \stackrel{D}{\longrightarrow }\int _0^1Q_2^2(r)dr\\ y_ t=\mu +\delta t+X_ t'\beta + u_ t:\qquad & \widehat{\mi{LM}}_\tau \stackrel{D}{\longrightarrow }\int _0^1Q_3^2(r)dr \end{align*}