Is a sufficient estimator unbiased?
Any estimator of the form U = h(T) of a complete and sufficient statistic T is the unique unbiased estimator based on T of its expectation. Hence, if T is complete and sufficient, U = h(T) is the MVUE of its expectation.
Why is the RAO-Blackwell theorem useful?
The Rao-Blackwell theorem is one of the most important theorems in mathematical statistics. It asserts that any unbiased estimator is improved w.r.t. variance by an unbiased estimator which is a function of a sufficient statistic.
Is the Rao Blackwell estimator better than the original?
The improved estimator is unbiased if and only if the original estimator is unbiased, as may be seen at once by using the law of total expectation. The theorem holds regardless of whether biased or unbiased estimators are used. The theorem seems very weak: it says only that the Rao–Blackwell estimator is no worse than the original estimator.
What is the mean squared error of Rao Blackwell?
The mean squared error of an estimator is the expected value of the square of its deviation from the unobservable quantity being estimated. The mean squared error of the Rao–Blackwell estimator does not exceed that of the original estimator.
Which is more general version of the Rao-Blackwell theorem?
Convex loss generalization. The more general version of the Rao–Blackwell theorem speaks of the “expected loss” or risk function : where the “loss function” L may be any convex function. If the loss function is twice-differentiable, as in the case for mean-squared-error, then we have the sharper inequality.
Which is an example of an improvable Rao-Blackwell improvement?
An example of an improvable Rao–Blackwell improvement, when using a minimal sufficient statistic that is not complete, was provided by Galili and Meilijson in 2016. Let . In the search for “best” possible unbiased estimators for