Page 231 - Special Topic Session (STS) - Volume 2

STS486 Alessandro F. et al.
where the first penalty term controls the number of ≠ 0 and the second one

controls smoothness of ; hence identifying temporary and permanent

changes of Section 1.
In practice the choice of and for step changes and for impulses may
2
1
be quite different. Hence, we will focus on the former problem.
In Equation (6) ; an important case is = 0, known as mean filtering in
1
signal processing (e.g. Ottersten et al., 2016). In this case, we rewrite Equation
(6) in matrix form
2
‖ − ‖ + ‖‖
2
2
1
where is the first order difference. Hence reparametrizing = , we have
2
‖ − −1 ‖ + ‖‖ (7)
2 2 1
Nonetheless, optimising Equation (6) with SLEP package (Liu et al., 2010 and
2015) is computationally more efficient than optimising Equation (7) with
lasso function of Matlab package. Moreover preliminary results show that it
is also more stable and flexible. Infact may be optimised using CV, giving
1
small but non-null > 0.
1
̂
Harmonisation After are estimated, say , the harmonised measurement

are obtained by
̂
∗
= −

with harmonisation uncertainty
̂
( )

which may be approximately computed using Theorem 1 of Tibshirani et
al. (2005).

References
1. Grillenzoni C. (1994) Optimal recursive estimation of dynamic models.
Journal of the American Statistical Association. 89:427. 777-787.
2. Grillenzoni C. (1997) Recursive generalized M-estimators of system
parameters. Technometrics. 39:2, 211-224.
3. Haimberger, L., Tavolato, C., Sperka, S., (2012) Homogenization of the
global radiosonde temperature dataset through combined comparison
with reanalysis background series and neighboring stations. J. Clim. 25,
8108.8131.
4. Liu J., Ji S., and Ye J. (2015) SLEP: Sparse Learning with Efficient
Projections, Version 4.1. https://github.com/divelab/SLEP.
5. Liu J., Yuan L, and Ye J., (2010) An Efficient Algorithm for a Class of Fused
Lasso Problems, KDD.
6. Ottersten J., Wahlberg B., Rojas C.R., (2016) Accurate Changing Point
Detection for l1 Mean Filtering, IEEE SIGNAL PROCESSING LETTERS, 23:2,
297-301.

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