Question

A good point estimator is said to be unbiased and have a large standard deviation a)...

A good point estimator is said to be unbiased and have a large standard deviation
a) true
b) false
Math   Statistics-And-Probability   
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Answer #1

A good point estimator should have the following properties :

a) Unbiasedness : The expected value of the estimator should be equal to the parameter

b) Consistency : This means that as n increases the value of the point estimator nears the parameter.

c) Efficiency : It means that the point estimator should have the smallest variance (or standard deviation) among all the estimators

d) Sufficiency : It should capture as much information about the parameter.

The statement is false as the standard deviation of the point estimator cannot be large. This will violate the criteria of efficiency

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