The mathematical results which you are asked to prove in this problem were evidenced numerically in the two problems above. Given a kernel function K and n couples (x1, y1), ... , (xn, yn) of real numbers, compute the limits:
of the kernel smoother when the bandwidth goes to 0 or ∞.
You can choose one of the four kernel functions given in the text (pick your favorite) or you can try to give this proof for a general kernel function if you feel comfortable enough.