Multidimensional autoregression |

In Chapter ,
subroutine `invint1()`
solved the problem of inverse linear interpolation,
which is,
given scattered data points,
to find a function on a uniform mesh
from which linear interpolation gives the scattered data points.
To cope with regions having no data points,
the subroutine requires an input roughening filter.
This is a bit like specifying a differential equation
to be satisfied between the data points.
The question is, how should we choose a roughening filter?
The importance of the roughening filter
grows as the data gets sparser or as the mesh is refined.

Figures 22-25 suggest that the choice
of the roughening filter need not be subjective,
nor a priori,
but that the prediction-error filter (PEF) is the ideal roughening filter.
Spectrally, the PEF tends to the inverse of its input
hence its output tends to be ``level''.
Missing data that is interpolated with this ``leveler''
tends to have the spectrum of given data.

- Test results for leveled inverse interpolation
- Analysis for leveled inverse interpolation
- Seabeam: theory to practice
- Risky ways to do nonlinear optimization
- The bane of PEF estimation

Multidimensional autoregression |

2013-07-26