In this video, the question of finding the lower bound on the performance of all estimators for a particular
probabilistic problem, as a benchmark with which to compare the
performance of a given estimator. The Cramer-Rao lower bound (CRLB) is
introduced in this video for this benchmark, for the class of unbiased
estimators. The Fisher Information is discussed, and it is shown how to
test for the existence of a minimum variance unbiased estimator (MVUE)
which attains the CRLB. An example is shown for deriving the sample
mean, which is a MVUE (and as a result also the mean square error (MSE)
estimator). In the example, the minimum variance is found through the
two alternate but equivalent expressions for the CRLB.
PGEE11164 Probability, Estimation Theory, and Random Signals Lectures -- School of Engineering, University of Edinburgh. Copyright James R. Hopgood and University of Edinburgh, Scotland, United Kingdom (UK). 2020.
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