An interpretation of the moore-penrose generalized inverse of a singular fisher information matrix
Journal
IEEE Transactions on Signal Processing
Journal Volume
60
Journal Issue
10
Pages
5532-5536
Date Issued
2012
Author(s)
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. 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 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. © 2012 IEEE.
Subjects
Constrained parameters; Cramér-Rao bound (CRB); Singular Fisher information matrix (FIM)
Other Subjects
Constrained parameters; Constraint functions; Joint designs; Lower bounds; Minimum variance; Moore-Penrose generalized inverse; Parametric estimation; Performance bounds; Singular fisher information; Unbiased estimator; Unknown parameters; Estimation; Fisher information matrix
Type
journal article