In: Statistics and Probability
MLE stands for maximum likelihood estimate.
Not only in the case of regression but in general, maximum likelihood estimate means that you just maximize the likelihood. This does not specify that the likelihood has to be produced by IID sampling or the error distribution has to be IID.
And if the sampling is dependent or the distribution of the error is dependent then you can modify the MLE accordingly.
Following my help you in understanding better,
And here you may have to find any such function g which is other than NORMAL.