2.2 Properties of estimators

The definition of an estimator makes no mention of a correspondence between the estimator and the parameter of interest. Of course, in reality we would like our estimators to be ‘good’ in the sense that they generally give estimates that are ‘close’ to the parameter we are interested in.

There are three properties of estimators that we are generally interested in

1. 1.

   Expectation, $𝔼[\widehat{\theta }]$;

2. 2.

   Variance, $\mathrm{Var}(\widehat{\theta })$, and in particular what happens to the variance as the sample size increases ($n\to \mathrm{\infty }$);

3. 3.

   Sampling distribution.