Suppose that $Y_1, Y_2, \dots, Y_n$ are random variables with progressively decreasing bias. We want to solve for $d$ which is the number of random variables we leave out. How and can I find a closed form solution to this problem?
Let function $\hat{f} : \{0,1,\dots,n\} \to \Bbb R$ be defined by
$$ \hat{f}(d) := \frac1{n-d} \sum_{i=d+1}^n Y_i $$
Let
$$ \mbox{MSER} := \frac{1}{(n-d)^2} \sum_{i=d+1}^n \left( Y_i - \hat{f}(d) \right)^2 $$
How do I minimize MSER w.r.t. to $d$?
I know that I need to take the first derivative of MSER w.r.t. to $d$,but that's as far as I've gotten.