A Note on Properties of Iterative Procedures of Asymptotic Inference

This note deals with the article 'On iterative procedures of asymptotic inference' by K.O. DZHAPARIDZE (1983), in which an informal discussion is given on performing an unconstrained maximization or solving non–linear equations of statistics by iterative methods with the quadratic termination property. It discusses the theorem that if a maximized function, e.g. the likelihood function, is asymptotically quadratic, then for asymptotically efficient inference finitely many iterations are needed.
It is argued here that the theory still applies if certain well specified inexact (hence computationally cheaper) line searches are used in the optimization.