= Sandwich variance of an M-estimator
{title2=$V=A^{-1}BA^{-T}$}
For an estimating equation with population root $\theta=T(F)$, let $A=\mathbb E_F\partial_\theta\psi(X,\theta)$ be nonsingular and $B=\mathbb E_F[\psi\psi^T]$. Differentiating the contaminated population equation gives <influence function> $-A^{-1}\psi(x,\theta)$. A consistent sample root with differentiable local expansion satisfies $\sqrt n(\widehat\theta-\theta)=-A^{-1}n^{-1/2}\sum_i\psi(X_i,\theta)+o_p(1)$, so the <central limit theorem> gives the displayed <covariance>. In the scalar case this is $\mathbb E\psi^2/A^2$.
Back to article page