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In-Depth Information
LGSS Algorithm
,
α
1. Let
t
be the number of observation time points. Let
α
2
be two user-
1
S =
0, the set of
saved
models
. Let us identify any
t
-expanded matrix with the set of vectors con-
stituted by its columns;
2. Compute the matrices
defined significance values for partial F-tests. Let
of the
t
-expansions of substance differences
and of regressors, respectively;
3. Compute the log-gain scores for all the (expanded) regressors of
D
,
G
G
,and
G
be the subset/submatrix
sort them accordingly in decreasing order. Let
having the best log-gain scores (according to a prefixed
user-defined threshold);
4. Let
of regressors of
G
G
, and compute the
M
be a user-defined initial subset/submatrix of
following LSE of unknown values
vec
(C)
:
(A
⊗
M)
×
vec
(C)=
vec
(D)
(3.45)
5. For each expanded regressor
g
t
∈
G
/
M
, compute the LSE of Eq. (3.45),
g
t
where
M=M
∪{
}
, then compute the partial F-test of the extended model
g
t
, according to Eq.(3.43);
6. Is there some model, among those computed at the previous step, having
a partial F-test value higher than the value of (3.44) where
M
∪{
}
with respect to the current model
M
α
=
α
1
?IfNo,
then go to step 11;
7. Update
as the model, among those of step 5, having the highest value of
partial F-test;
8. For each regressor
g
t
M
∈
M
, compute the LSE of Eq. (3.45), where
M =
g
t
M
/{
}
, and then compute the partial F-test of the current model
M
with
g
t
, according to Eq.(3.43);
9. Is there some model, among those computed at the previous step, having a
F-test value lower than the value of (3.44) where
respect to the reduced model
M
/{
}
α
=
α
2
? If No, then go to
step 5;
10. Update
as the model, among those of step 8, having the lowest value of
partial F-test, then go to step 5;
11. Add the current model
M
M
to the set
S
of saved models;
G
= G
G
as
G
∪{
g
t
,where
g
t
12. Is
? If No, then update
}
is the expanded
G
/
G
having the highest log-gain score, and go
regressor among those in
to step 5;
13. Among the models of
select the best one, by using the indexes of
Eqs. (3.35), (3.36), (3.37), (3.39);
14. Provide as output the model selected at the previous step with its evaluation
of parameters and confidence intervals of regressors coefficients.
S
