Exploring estimator bias-variance tradeoffs using the uniform CRbound
Hero, A.O., III
Fessler, J.A.
Usman, M.
Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI;
This paper appears in: Signal Processing, IEEE Transactions on
Publication Date: Aug 1996
Volume: 44,
Issue: 8
On page(s): 2026-2041
ISSN: 1053-587X
References Cited: 51
CODEN: ITPRED
INSPEC Accession Number: 5361520
Digital Object Identifier: 10.1109/78.533723
Current Version Published: 2002-08-06
Abstract
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
Index
Terms
Available to subscribers and IEEE members.
References
Available to subscribers and IEEE members.
Citing Documents
Available to subscribers and IEEE members.
Cart
