Chapter 3 Point estimation

Definition 3.1 (Estimation) Estimation is the process of infering or attempting to guess the value of one or several population parameters from a sample. Therefore, an estimator \(\hat\theta\) of a parameter \(\theta\in\Theta\) is an statistic with range in the parameter space \(\Theta.\)

Example 3.1 The following table shows the usual estimators for well-known parameters.

Parameter Estimator
Proportion \(p\) Sample proportion \(\bar{X}\)
Mean \(\mu\) Sample mean \(\bar{X}\)
Variance \(\sigma^2\) Sample variance \(S^2\) and sample quasivariance \(S'^2\)