The kernel estimate can be generalized to product kernels. Let K∗ j (j = 1, 2,...,d) be kernels defined on R and hn1,...,hnd bandwidth sequences. Put                        Kn(x − z) = 6d j=1 K∗ j xj...

The kernel estimate can be generalized to product kernels. Let K∗ j (j = 1, 2,...,d) be kernels defined on R and hn1,...,hnd bandwidth sequences. Put

                       Kn(x − z) = 6d j=1 K∗ j xj − zj hnj  .

Formulate consistency conditions on hn1,...,hnd.

Extend Theorem 5.2 to product kernels:

                   Emn − m2 ≤ cˆ n 2d j=1 hnj + C2 d j=1 h2 nj .