Alternative Equation Formats

$${\displaystyle \begin{array}{ll}{r}_w(b)& =\underset{{\mathrm{\Delta <!--\; \Delta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_i=1}{\sum <!--\; \sum \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}{\mathrm{\rho <!--\; \rho \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_{{\mathrm{\tau <!--\; \tau \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_k}(Y_i-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>x_i^{\prime }b)\\ & +\underset{{\mathrm{\Delta <!--\; \Delta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_i=0}{\sum <!--\; \sum \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}\{w_i({\mathrm{\tau <!--\; \tau \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_k){\mathrm{\rho <!--\; \rho \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_{{\mathrm{\tau <!--\; \tau \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_k}(Y_i-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>x_i^{\prime }b)+(1-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>w_i({\mathrm{\tau <!--\; \tau \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_k)){\mathrm{\rho <!--\; \rho \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_{{\mathrm{\tau <!--\; \tau \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_k}(Y^{\ast <!--\; \ast \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>x_i^{\prime }b)\}\end{array}}$$

$${\displaystyle \begin{array}{ll}{r}_w(b)& =\underset{{\mathrm{\Delta <!--\; \Delta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_i=1}{\sum <!--\; \sum \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}{\mathrm{\rho <!--\; \rho \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_{{\mathrm{\tau <!--\; \tau \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_k}(Y_i-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>x_i^{\prime }b)\\ & +\underset{{\mathrm{\Delta <!--\; \Delta \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_i=0}{\sum <!--\; \sum \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}\{w_i({\mathrm{\tau <!--\; \tau \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_k){\mathrm{\rho <!--\; \rho \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_{{\mathrm{\tau <!--\; \tau \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_k}(Y_i-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>x_i^{\prime }b)+(1-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>w_i({\mathrm{\tau <!--\; \tau \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_k)){\mathrm{\rho <!--\; \rho \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_{{\mathrm{\tau <!--\; \tau \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}}_k}(Y^{\ast <!--\; \ast \; --><span\; class="Comment\_comment\_\_N0+Yl"></span>}-<!--\; -\; --><span\; class="Comment\_comment\_\_N0+Yl"></span>x_i^{\prime }b)\}\end{array}}$$

\[ \begin{array}{lll} r_ w(b) & =\sum _{\Delta _ i=1} \rho _{\tau _ k}(Y_ i - {x}_ i' { b})\\ & +\sum _{\Delta _ i=0} \left\{ w_{i}(\tau _ k) \, \rho _{\tau _ k}(Y_ i - {x}_ i' b) + (1 - w_{i}(\tau _ k)) \rho _{\tau _ k}(Y^* - { x}_ i' b) \right\} \end{array} \]