Smooth functions and local extreme values
Given a sample of observations
at time points
we consider the problem of specifying a function
such that
 is smooth,
 fits the data in the sense that the residuals
satisfy the multiresolution criterion

(1) 
 is as simple as possible so that exhibits the minimum number of
local extreme values.
We analyse in particular a fast method
which is based on minimising
where the are chosen automatically.
The new method can also be applied to density estimation.