5/30/2015

Topics

Accuracy

Regularization

Efficiency

Accuracy

Assume a is "small"

Least squares

Ths SVD lets us solve least squares problems using the direct approach

Doornik's VECM Example











Naive Johansen method can exhibit complete loss of accuracy when \(\delta \approx 10^{-6}\).

Regularization

Subspace projection

Reduce influence of noise by projecting into a "less-noisy" subspace.

SVD is one way to define such subspaces.

Example: exact system

Example: perturbed system

Wild exact solution

Chill projected solution

Thresolded precision matrix

Regularized

Ill-posed problems

P.C. Hansen's PPTSVD

Efficiency

Projection methods turn big data into data

IRLBA directed network centrality

Projected LMM

Turns large \(n\times n\) LMM into a series of easy \(n\times 1\) LMMs.

References