201. An Interpretation of the Moore-Penrose Generalized Inverse of a Singular Fisher Information Matrix
- Author
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Li, Yen-Huan and Yeh, Ping-Cheng
- Subjects
Computer Science - Information Theory ,Mathematics - Statistics Theory - Abstract
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. Cramer-Rao bound (CRB), a popular tool to lower bound the variances of unbiased estimators, seems inapplicable in such situations. In this paper, 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 minimum constraint functions. This result ensures the logical validity of applying the Moore-Penrose generalized inverse of an FIM as the covariance lower bound when the FIM is singular. Furthermore, the result can be applied as a performance bound on the joint design of constraint functions and unbiased estimators., Comment: 10 pages, accepted for publication in IEEE Transactions on Signal Processing
- Published
- 2011
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