Could anyone help me with the part of this question highlighted in the link? I can derive the first part, but i'm having problems canceling alpha, any help would be greatly appreciated!
Let Q be the function you want to minimize.
Just solve the simultaneous equation and in the usual way.
Alternatively, we might notice that in the usual matrix notation
where and solve with matrix calculus.
An obvious application is where we think that the variance grows proportionally with , so we could take