Matrix analysis
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Minimum bias multiple taper spectral estimation
IEEE Transactions on Signal Processing
Minimum variance in biased estimation: bounds and asymptotically optimal estimators
IEEE Transactions on Signal Processing
Parameter estimation problems with singular information matrices
IEEE Transactions on Signal Processing
Exploring estimator bias-variance tradeoffs using the uniform CRbound
IEEE Transactions on Signal Processing
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This paper extends the work of Y. C. Eldar, "Minimum variance in biased estimation: Bounds and asymptotically optimal estimators," in IEEE Trans. Signal Process., vol. 52, pp. 1915-1929, Jul. 2004, which deals with only nonsingular Fisher information matrix. In order to guarantee the uniform Cramér-Rao bound to be a finite lower bound and also to have a feasible solution to the optimization problem in the work of Y. C. Eldar, it is proved that the norms of bias gradient matrices of all biased estimators must have a nonzero exact lower bound, which mainly depends on the rank of the singular Fisher information matrix. The smaller the rank of the singular Fisher information matrix is, the larger the lower bound of norms of bias gradient matrices of all biased estimators is. For a specific Frobenins norm, the exact lower bound is simply the difference between the parameter dimension and the rank of the singular Fisher information matrix.