Least Absolute Deviation Estimator

Definition

Consider a Simple Linear Regression model $Y_i={\beta }_0+{\beta }_1{X}_i+{ϵ}_i$ The least absolute deviation estimator ${\hat{\beta }}_0,{\hat{\beta }}_1$ are the estimator that minimize $\sum _{i=1}^n|{ϵ}_i|=\sum _{i=1}^n|Y_i-{\beta }_0+{\beta }_1{X}_i|$