Question

For estimating a population characteristic, why is an unbiased statistic with a small standard error preferred over an unbiased statistic with a larger standard error?

Answer 1

Estimators are used to estimate population parameters a estimator with large variance implies that it is more fluctuating from the original value or in other words it can give estimate far from the original value or in other words confidence interval for this will be more wider which is not a good thing but for a estimator with small variance means it is not more fluctuating it can lie near the actual value of parameter it gives us a shorter confidence interval