Properties of Point Estimators

Consider three marksmen,

Here we have three different situations.

• Target 1 has all its shots clustered tightly together, but none of them hit the bullseye.
• Target 2 has a large spread, but on average the bullseye is hit.
• Target 3 has a tight cluster around the bullseye.

In statistical terminology, we say that

• Target 1 is biased/ with a small variance.
• Target 2 is unbiased/ with a large variance.
• Target 3 is unbiased/ with a small variance.

If you were hiring for the police department, which shooter would you want? In general in statistics, we want both unbiased and small variance--an estimator that almost always is ``on target.''