Introduction
An estimator, noted \(\hat{\theta}\) , is a function of random variables. As such, it has a hope \(E\left[\hat{\theta}\right]\) and a variance \(Var\left(\hat{\theta}\right)\). The main purpose of the statistical estimate is to check the error between the \(\hat{\theta}\) estimator and the true value of the parameter to be estimated, \(\theta\) . Although people sometimes interpret the estimator as a random variable, this interpretation can be misleading if not clearly specified.
The quality of estimators is expressed in their convergence, bias, effectiveness, and robustness. Different methods make it possible to obtain estimators of different qualities.