# Differentiuating Between Unbiased Estimators

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When choosing an estimator for a statisitical parameter we are primarily interested in simplicity of calculation and the bias of the estimator.

The bias of a statisitical parameter is the difference between the estimator for the parameter and the true value of the parameter. If the estimator for a population parameteristhen

We are usually interested in selecting the estimator with the smallest bias, since it will be closer to the actual value of the population parameter more often on average that any other estimator.

Suppose we are interested in finding an estimator for the population mean,We have a choice of estimators:

whereandare individual measurements from the population

whereandare individual measurements from the population

Each of these estimators is unbiased, since

If the variance ofisthen the variance ofis

and the variance ofis

Of all these estimators forhas the smaller variance, sois the best estimator.