Solution Found!
Suppose that Which estimator is better and in what sense
Chapter 7, Problem 28E(choose chapter or problem)
Suppose that \(\hat{\Theta}_{1}\) and \(\hat{\Theta}_{2}\) are unbiased estimators of the parameter \(\theta\). We know that \(V\left(\hat{\Theta}_{1}\right)=10\) and \(V\left(\hat{\Theta}_{2}\right)=4\). Which estimator is better and in what sense is it better? Calculate the relative efficiency of the two estimators.
Equation Transcription:
Text Transcription:
Theta hat_1
Theta hat_2
theta
V(Theta hat_1)=10
V(Theta hat_2)=4
Questions & Answers
QUESTION:
Suppose that \(\hat{\Theta}_{1}\) and \(\hat{\Theta}_{2}\) are unbiased estimators of the parameter \(\theta\). We know that \(V\left(\hat{\Theta}_{1}\right)=10\) and \(V\left(\hat{\Theta}_{2}\right)=4\). Which estimator is better and in what sense is it better? Calculate the relative efficiency of the two estimators.
Equation Transcription:
Text Transcription:
Theta hat_1
Theta hat_2
theta
V(Theta hat_1)=10
V(Theta hat_2)=4
ANSWER:
Solution:
Step 1 of 2:
Let and
are unbiased estimator of the parameter
.
With V( )= 10, and V(
)=4.
We have to find which estimator is better. We also have to find the relative efficiency of two estimators.