Exploring estimator bias-variance tradeoffs using the uniform CRbound
Hero, A.O., III; Fessler, J.A.; Usman, M.
Signal Processing, IEEE Transactions on
Volume 44, Issue 8, Aug 1996 Page(s):2026 - 2041
Digital Object Identifier 10.1109/78.533723
Summary:We introduce a plane, which we call the delta-sigma plane, that is
indexed by the norm of the estimator bias gradient and the variance of
the estimator. The norm of the bias gradient is related to the maximum
variation in the estimator bias function over a neighborhood of
parameter space. Using a uniform Cramer-Rao (CR) bound on estimator
variance, a delta-sigma tradeoff curve is specified that defines an
“unachievable region” of the delta-sigma plane for a
specified statistical model. In order to place an estimator on this
plane for comparison with the delta-sigma tradeoff curve, the estimator
variance, bias gradient, and bias gradient norm must be evaluated. We
present a simple and accurate method for experimentally determining the
bias gradient norm based on applying a bootstrap estimator to a sample
mean constructed from the gradient of the log-likelihood. We demonstrate
the methods developed in this paper for linear Gaussian and nonlinear
Poisson inverse problems
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