We shall introduce PHD today.
Hwo to distinguish nonlinear functions from linear functions?
The key is the second derivatives. For linear functions,
they must be equal to zero. The method of Principal Hessian direction
(PHD) explores this fact in higher dimensional space for finding
e.d.r. directions. PHD looks for the most bending directions
for the response surface in some average sense.
1. definition of PHD
2. A proof of an invariance property of PHD
3.Stein lemma
4. The main theorem
5. Sample version of PHD; y-based and r-based. We shall consider
r-based method from now on.