Properties of quadratic covariance bounds

We investigate the properties of quadratic covariance bounds for parametric estimators. The Cramer-Rao, Bhattacharyya (1946), and Barankin (1949) bounds have this quadratic structure and the properties of these bounds are uniquely determined by their respective score functions. We enumerate some characteristics of score functions which generate tight bounds. We also introduce projection operator and integral/kernel representations for this class of quadratic covariance bounds. These representations are useful as analysis and synthesis tools. We also address the issue of efficiency for this class of bounds.<
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