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How do you show that a statistic is complete?
Definition: A statistic T is called complete if E[g(T)]=0 for all and some function g implies that P(g(T)=0)=1 for all.
What is MOUE in statistics?
In statistics a minimum-variance unbiased estimator (MOUE) or uniformly minimum-variance unbiased estimator (REVUE) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter.
How is Revue calculated?
Hence, the REVUE of is h(X(n)) = g(X(n)) + n1X(n)g(X(n)). In particular, if =, then the REVUE of is (1 + n1)X(n).
What statistic is the best unbiased estimator for u?
function of T(X). Therefore, X is the best unbiased estimator for µ.
What does it mean for an estimator to be efficient?
An efficient estimator is the “best possible” or “optimal” estimator of a parameter of interest. The definition of “best possible” depends on one's choice of a loss function which quantifies the relative degree of undesirability of estimation errors of different magnitudes.
Is Revue unique?
1 Answer. Generally, an REVUE is essentially unique. The estimator you provided is not an REVUE though, indeed it is not even unbiased!! Notice that E[1X]=1E[X]=1p provided that our random variable is a Bernoulli with parameter p.
Does a minimal sufficient statistic always exist?
If there exists a minimal sufficient statistic, and this is usually the case, then every complete sufficient statistic is necessarily minimal sufficient(note that this statement does not exclude the option of a pathological case in which a complete sufficient exists while there is no minimal sufficient statistic).
How do you find minimal sufficient statistics?
A sufficient statistic T : X T is minimal sufficient if for any sufficient statistic U : X U there is a measurable function g : UT such that T = g(U) ex|(· |)-a.s. for all .
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