Necessary and sufficient conditions for local second order identifiability

We discuss the nature of the equivalence of (1) the nonsingularity of the asymptotic information matrix of a given process, i.e. the limit of the Hessian matrix (with respect to the parameter ??) of the log likelihood function and (2) local identifiability of the parameter ??. Second order local identifiability is given a structural definition related to those of [3], [5], [6]. The proof of the main equivalence theorem differs from that of Rothenberg [6] in that it does not involve differential equations.