There are several requirements that we might impose on an estimator function. One is that the estimator must be consistent.  This means that for larger samples the estimator function \(\hat{\theta}\) converges to the parameter values associated with the distribution \(\theta^{\star}\) of the data generating system, or the true parameter values for short. Another requirement is that the estimator must be unbiased, meaning that there is no discrepancy between the expected value of the estimator and the true parameter values. The MLE procedure is certainly not the only one used for estimating the value of a parameter of interest on the basis of statistical data. A simpler technique is the minimization of a particular target function, e.g., the minimizing the sum of the squares of the distances between the prediction of the statistical hypothesis and the data points, also known as the method of least squares.  A more general perspective, first developed by Wald (1950), is provided by measuring the discrepancy between the predictions of the hypothesis and the actual data in terms of a loss function. The summed squares and the likelihoods may be taken as expressions of this loss.