Necessary and sufficient conditions for local second-order identifiability
Robert Kent Goodrich, Peter E. Caines · IEEE Transactions on Automatic Control · 1979
This note presents a new formulation and proof of the result the Hessian of the likelihood function of an observed process at the point\thetain a parameter space, computed under the assumption that the process is i.i.d. Gaussian, is asymptotically nonsingular if and only if\thetais locally second-order identifiable. That is to say, if and only if the parameters in a neighborhood of\thetaare in one-to-one correspondence with the second-order statistics of the observed process.