Support for EM estimation of MixAR models, internal function.
mixSubsolve.Rd
Solve the linear sub-system arising in the M-step of the EM algorithm for MixAR models with Gaussian noise components. This gives estimates of the parameters of the \(k\)th AR component of the model.
Arguments
- k
which component, an integer.
- pk
AR order of the \(k\)th component.
- Stau,Stauy,Stauyy
sums and cross-sums needed to form the system.
- shift
If
TRUE
, estimate also a shift, otherwise set the shift to 0.- tol
tolerance, only used in case of trouble, see Details.
Details
mixSubsolve
forms and solves a linear subsytem to obtain
estimates of the AR parameters (and the shift, if shift
is
TRUE
) for the k
-th MixAR component.
First, solve()
is tried. If it reports that the system is
(numerically) singular, a solution is computed using SVD with
tolerance tol
.
Note that argument tol
is not used in the call to
solve()
. The net effect is that solve()
computes the
solution with its very small default tollerance. Probably I wanted
discontinuity during optimisation, which could result if using a
larger tolerance, and only resort to that if absolutely needed.
I don't remember why I used pseudo-inverse in mixSubsolve()
,
when solve()
has a similar tol
argument for its
QR-decomposition.