Econometric applications of positive rank-one modifications of the symmetric factorization of a positive semi-definite matrix

We present an algorithm for updating the symmetric factorization of a positive semi-definite matrix after a positive rank-one modification, which works even if the matrices involved do not have full rank. Recursive least squares and factor analysis provide two important econometric applications. An illustrative simulation shows that it can be potentially very useful in recursive situations.Recursive least squares, factor analysis, Cholesky decomposition, multicollinearity