Are there regression models where variance is the outcome, not mean? For instance, for interquartile range I may use quantile regression. But is there something similar for variance?
For example, let us have observations $(X_1,Y_1),\dots,(X_N,Y_N)$, where $Y_j$ are sampled from the normal distributions $N(a+bX_j,\ c+dX_j)$, respectively. Are there regression methods that allow us to estimate the parameters $a,b,c,d$?