{\displaystyle {\begin{aligned}{\widehat {\theta }}_{2}&={\frac {Y_{1}+Y_{2}-Y_{3}-Y_{4}+Y_{5}+Y_{6}-Y_{7}-Y_{8}}{8}}.\\[5pt]{\widehat {\theta }}_{3}&={\frac {Y_{1}+Y_{2}-Y_{3}-Y_{4}-Y_{5}-Y_{6}+Y_{7}+Y_{8}}{8}}.\\[5pt]{\widehat {\theta }}_{4}&={\frac {Y_{1}-Y_{2}+Y_{3}-Y_{4}+Y_{5}-Y_{6}+Y_{7}-Y_{8}}{8}}.\\[5pt]{\widehat {\theta }}_{5}&={\frac {Y_{1}-Y_{2}+Y_{3}-Y_{4}-Y_{5}+Y_{6}-Y_{7}+Y_{8}}{8}}.\\[5pt]{\widehat {\theta }}_{6}&={\frac {Y_{1}-Y_{2}-Y_{3}+Y_{4}+Y_{5}-Y_{6}-Y_{7}+Y_{8}}{8}}.\\[5pt]{\widehat {\theta }}_{7}&={\frac {Y_{1}-Y_{2}-Y_{3}+Y_{4}-Y_{5}+Y_{6}+Y_{7}-Y_{8}}{8}}.\\[5pt]{\widehat {\theta }}_{8}&={\frac {Y_{1}+Y_{2}+Y_{3}+Y_{4}+Y_{5}+Y_{6}+Y_{7}+Y_{8}}{8}}.\end{aligned}}}