5.2. We can apply two-dimensional kernel analysis directly, as well as using ASH. This is most straightforward for the normal kernel aligned with axes, that is with variance diag(h²x, h²y) . Then the kernel estimate is

which can be evaluated on a grid as XyT where Xis = ¢ ((gxi - X s) / hx)
and (gxi) are the grid points, and similarly for y. Write a function kde2d to implement this, and try it on the f ai thful examples. How would you choose the bandwidths?

f(x,y) = , ((xx)/h) ((y-ys)/hy) nhng