The Gaussian Maximum-Likelihood Estimator Versus the Optimally Weighted Least-Squares Estimator [Lecture Notes]

In this lecture note, we derive and compare the asymptotic covariance matrices of two parametric estimators: the Gaussian maximum-likelihood estimator (MLE) and the optimally weighted leastsquares estimator (LSE). We assume a general model parameterization where the model's mean and variance are jointly parameterized and consider Gaussian and non-Gaussian data distributions.