Support for EM estimation of MixAR models, internal function.

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.

Usage

mixSubsolve(k, pk, Stau, Stauy, Stauyy, shift, tol = 1e-07)

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.

Author

Georgi N. Boshnakov