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