论文信息 - On the identifiability of parameters

On the identifiability of parameters

A precise definition of identifiability of a parameter is given in terms of consistency in probability for the parameter estimate. Under some mild Uniformity assumptions on the conditional density parameterized by the unknown parameter, necessary and sufficient conditions for the unknown parameter to be identifiable are established. The assumptions and identifiability criteria are expressed in terms of the density of individual observations, conditioned upon all past observations. The results are applied to linear system identification problems.

E. Tse | J. Anton

[1] V. S. Huzurbazar,et al. The likelihood equation, consistency and the maxima of the likelihood function. , 1948, Annals of eugenics.

[2] Abraham Wald,et al. Asymptotic Properties of the Maximum Likelihood Estimate of an Unknown Parameter of a Discrete Stochastic Process , 1948 .

[3] A. Wald. Note on the Consistency of the Maximum Likelihood Estimate , 1949 .

[4] J. Wolfowitz. On Wald's Proof of the Consistency of the Maximum Likelihood Estimate , 1949 .

[5] E. E. Fisher. The identification of linear systems , 1965 .

[6] Masanao Aoki,et al. On observability of stochastic discrete-time dynamic systems☆ , 1968 .

[7] R. Mehra. Identification of stochastic linear dynamic systems , 1969 .

[8] M. Aoki,et al. On Certain Convergence Questions in System Identification , 1970 .

[9] Yaakov Bar-Shalom,et al. On the Asymptotic Properties of the Maximum-Likelihood Estimate Obtained from Dependent Observations , 1971 .