# LSE vs MLE - why use LSE when we have MLE?

I know that with linear regressions Least Squares Estimate (LSE) and Maximum Likelihood Estimate (MLE) have differences, in that (1) MLE does not use unbiased standard deviation(the denominator is n) (2) While LSE requires homogenous E(residuals|X) & V(residuals|X), MLE does not, (3) LSE and MLE get identical when the residuals of LSE follow N(0, sigma^2).

Considering that LSE requires further assumptions[(3)] to become MLE, it seems that MLE has more beneficial characteristics of being a statistical estimator. My question is, then, Why do we have to use LSE when we have MLE, since the computation on both coefficients doesn't seem to differ in their difficulty? Some colleagues of mine told me that deciding which to use differs by field and interests, but it seems to me that MLE serves better in nearly every aspect and at the same time computing MLE doesn't seem to be much more difficult. So, Why not MLE for every case rather than LSE?

• For linear regression, the result is the same. Feb 23, 2021 at 15:06