We often face singular matrices in practice: OLS with singular (X'X), GMM with singular weighting matrix, singular matrix in Wald statistics. I'm wondering how can we overcome this issue. I've seen two solutions used in different contexts:
1) Ridge regression: http://en.wikipedia.org/wiki/Tikhonov_regularization
2) Generalized inverse: http://en.wikipedia.org/wiki/Generalized_inverse
What do you think would be preferable to do when the estimator or test statistics depends on the inverse of a matrix which is singular?