EXPLORING ESTIMATOR BIAS-VARIANCE TRADEOFFS USING THE UNIFORM CR BOUND

We introduce a plane, which we call the delta-sigma plane, that is ind exed by the norm of the estimator bias gradient and the variance of th e estimator. The norm of the bias gradient is related to the maximum v ariation in the estimator bias function over a neighborhood of paramet er space, Using a uniform Cramer-Rao (CR) bound on estimator variance, a delta-sigma tradeoff curve is specified that defines an ''unachieva ble region'' of the delta-sigma plane for a specified statistical mode l, In order to place an estimator on this plane for comparison with th e delta-sigma tradeoff curve, the estimator variance, bias gradient, a nd bias gradient norm must be evaluated. We present a simple and accur ate method for experimentally determining the bias gradient norm based on applying a bootstrap estimator to a sample mean constructed from t he gradient of the log-likelihood, We demonstrate the methods develope d in this paper for linear Gaussian and nonlinear Poisson inverse prob lems.