Assume that XXXXXXXXXXholds (a formal proof is given in Chapter 5). Because the ψ(Yi −x ⊤ i β) are independent and identically distributed random variables with 0 mean and variance σ 2 ψ , we can...

Assume that (3.17) holds (a formal proof is given in Chapter 5). Because the ψ(Yi −x ⊤ i β) are independent and identically distributed random variables with 0 mean and variance σ 2 ψ , we can apply the classical central limit theorem for the right-hand side of (3.17), when the Noether condition in (3.18) is satisfied. Consider the particular case of ψ(x) ≡ sign(x) so that Mn reduces to the L1-norm estimator of β. Work out the expression for γ 2 in (3.19) in this case. For ψ(x) ≡ x, (3.17) is an identity for the least square estimator of β.