Hand written solution required

Problem 1 Higher order kernels When the density f is k-times continuously differentiable and a kernel K of order k is used in a kernel density estimator then 2 AMISE(f(.; h)) = MK (K ) nh K ! 11f ( 4 ) 12 2 . (a) (2 marks) Check that the AMISE is minimised by 1 ( k!) 21 1 1 1172 2k+1 hAMISE = n2 kuk(K) 211f( k) 1172 (b) (2 marks) Compute the AMISE when the bandwidth hAMISE is used