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Which of the following is not needed in the Lehmann-Scheffe theorem for constructing UMVU estimators T=T(V)

Which of the following statement is not true about optimality of estimators?

MS22 Class 22

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Sufficient Statistics, UMVU

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Answers

1
Which of the following statement is not true about optimality of estimators?
Bayesian criterion minimizes the weighted average MSE error wrt the prior.
There exists an estimator minimizing the MSE for all parameters.
Minimax criterion gives the best worse case MSE over the parameter space Θ.
UMVU considers unbiased estimators.
2
Which of the following is not needed in the Lehmann-Scheffe theorem for constructing UMVU estimators T=T(V)
T is unbiased
V is complete
V is sufficient
V is unbiased
3
What is not true about the sufficient statistics V=V(X)?
The conditional probability P(X=x|V=v) does not depend on θ.
The observation X is a sufficient statistic.
It contains all relevant information about the data.
There is at most one sufficient statistics for a given model.
4
Which of the following statments is correct?
There always exists an UMVU.
It is possible that a biased estimator has smaller MSE than an UMVU.
There always exists an unbiased estimator
If T is unbiased for θ then g(T) is unbiased for g(θ).
5
Why is it enough to consider only unbiased estimators depending on sufficient statistics V to find an UMVU?
For EθT=θ exists T*=T*(V): EθT*=θ and var(T)⩾var(T*).
Sufficient statistics are easy to compute.
For EθT=θ exists T*=T*(V): EθT*=θ and var(T)⩽var(T*).
Sufficient statistics are functions of other sufficient statistics.