From Van der Vaart's Asymptotics Statistics, we have the derivation of the asymptotics for the least square regression (Example 5.27). Now, the problem 16 of the same section regards the asymptotics for the least absolute deviation.

I copy and paste here the problem 16.

"In Example $5.27$, consider the asymptotic behavior of the least absolute-value estimator $\hat{\theta}$ that $\operatorname{minimizes} \sum_{i=1}^n\left|Y_i-\phi_\theta\left(X_i\right)\right|$."

I am wondering how we can extend the example 5.27 knowing that the absolute value is not differentiable?



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