We consider conditions in a nonlinear regression model for the consistency of the estimator obtained by minimizing the $L_1$-norm, i.e. the sum of absolute deviations.
"The Consistency of Nonlinear Regression Minimizing the $L_1$-Norm." Ann. Statist. 10 (1) 316 - 319, March, 1982. https://doi.org/10.1214/aos/1176345716