In the context of a linear model, presented below in matrix form Y = X + u , where X is a n

In the context of a linear model, presented below in matrix form

Y = Xβ+u,

where X is a n × q matrix, β is a q ×1 column vector, and both Y and u are n ×1 column vectors.

(a) Explain how estimation of the parameter vector by Maximum Likelihood would differ from estimation by Ordinary Least Squares.

(b) If the errors in the model are not Normally distributed are you able to make an argument that the Ordinary Least Squares estimator is asymptotically normally distributed? Be sure to make clear any arguments you rely on.

(c) Show how, in the context of the above model, Weighted Least Squares can be used to address the issue of heteroscedasticity.