Z-estimator

A Z-estimator is a root of an estimating equation. Under differentiability, identification, and a central limit theorem, its first-order expansion has sandwich covariance.

Suppose random continuous real functions have unique zeros. If pointwise convergence in probability gives opposite strict limiting signs at the two ends of every sufficiently small interval about the target, the intermediate value theorem traps their zeros in those intervals with probability tending to one. The limiting function need not be continuous and the random functions need not be monotone.