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MathML

\begin{aligned} δ & = (N - 3 - p^{⋆})^{\frac{1}{2}} [\frac{1}{2} \log (\frac{1 + ρ_{Y | (X_{1}, X_{- 1})}}{1 - ρ_{Y | (X_{1}, X_{- 1})}}) + \frac{ρ_{Y | (X_{1}, X_{- 1})}}{2 (N - 1 - p^{⋆})} (1 + \frac{5 + ρ_{Y | (X_{1}, X_{- 1})}^{2}}{4 (N - 1 - p^{⋆})} + \\ \frac{11 + 2 ρ_{Y | (X_{1}, X_{- 1})}^{2} + 3 ρ_{Y | (X_{1}, X_{- 1})}^{4}}{8 (N - 1 - p^{⋆})^{2}}) - \frac{1}{2} \log (\frac{1 + ρ_{0}}{1 - ρ_{0}}) - \frac{ρ_{0}}{2 (N - 1 - p^{⋆})}] \\ ν & = \frac{N - 3 - p^{⋆}}{N - 1 - p^{⋆}} [1 + \frac{4 - ρ_{Y | (X_{1}, X_{- 1})}^{2}}{2 (N - 1 - p^{⋆})} + \frac{22 - 6 ρ_{Y | (X_{1}, X_{- 1})}^{2} - 3 ρ_{Y | (X_{1}, X_{- 1})}^{4}}{6 (N - 1 - p^{⋆})^{2}}] \end{aligned}

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Math as LaTeX Source

\begin{align*} \delta & = (N-3-p^\star )^{\frac{1}{2}} \left[ \frac{1}{2} \log \left( \frac{1+\rho _{Y|(X_1,X_{-1})}}{1-\rho _{Y|(X_1,X_{-1})}} \right) + \frac{\rho _{Y|(X_1,X_{-1})}}{2(N - 1 - p^\star )} \left( 1 + \frac{5 + \rho ^2_{Y|(X_1,X_{-1})}}{4(N - 1 - p^\star )} + \right. \right. \\ & \quad \left. \left. \frac{11 + 2 \rho ^2_{Y|(X_1,X_{-1})} + 3 \rho ^4_{Y|(X_1,X_{-1})}}{8(N - 1 - p^\star )^2} \right) - \frac{1}{2} \log \left( \frac{1+\rho _0}{1-\rho _0} \right) - \frac{\rho _0}{2(N - 1 - p^\star )} \right] \\ \nu & = \frac{N-3-p^\star }{N-1-p^\star } \left[ 1 + \frac{4 - \rho ^2_{Y|(X_1,X_{-1})}}{2(N - 1 - p^\star )} + \frac{22 - 6 \rho ^2_{Y|(X_1,X_{-1})} - 3 \rho ^4_{Y|(X_1,X_{-1})}}{6(N - 1 - p^\star )^2} \right] \\ \end{align*}