An Interpretation of the Moore-Penrose Generalized Inverse of a Singular Fisher Information Matrix

@article{Li2012AnIO,
  title={An Interpretation of the Moore-Penrose Generalized Inverse of a Singular Fisher Information Matrix},
  author={Yen-Huan Li and Ping-Cheng Yeh},
  journal={IEEE Transactions on Signal Processing},
  year={2012},
  volume={60},
  pages={5532-5536}
}
It is proved that in a non-Bayesian parametric estimation problem, if the Fisher information matrix (FIM) is singular, unbiased estimators for the unknown parameter will not exist. Cramér-Rao bound (CRB), a popular tool to lower bound the variances of unbiased estimators, seems inapplicable in such situations. In this correspondence, we show that the Moore-Penrose generalized inverse of a singular FIM can be interpreted as the CRB corresponding to the minimum variance among all choices of… CONTINUE READING

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