VECTOR UNIFORM CRAMER-RAO LOWER BOUND (WedAmPO1)

Author(s) : Yonina Eldar (Technion, Israel)

Abstract : We develop a uniform Cramer-Rao lower bound (UCRLB) on the total variance of any estimator of an unknown deterministic vector of parameters, with bias gradient matrix whose norm is bounded by a constant. We consider two different measures of norm, leading to two corresponding bounds. When the observations are related to the unknown vector through a linear Gaussian model, Tikhonov regularization and the shrunken estimator are shown to achieve the UCRLB. For more general models, we show that the penalized maximum likelihood estimator with a suitable penalizing function {\em asymptotically} achieves the UCRLB.

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