Signal Processing

The estimator's variance, which is written as \(Var\left(\hat{\theta}\right)\), shows how spread out the calculator's values are around its average. This shows how well it estimates the parameter \(\theta\) . This measurement is obtained by taking the average of the squares of the differences between each observation of the estimator and its average, thus allowing us to evaluate the variability of the assessor.

\(Var\left(\hat{\theta}\right)\equiv\sigma_E^\mathrm{2}=E\left[\left(\hat{\theta}-E\left(\hat{\theta}\right)\right)^\mathrm{2}\right]\) (2)

\(E\left(\hat{\theta}\right)\) represents the expectation of the estimator \(\hat{\theta}\).