An efficient algorithm for REML in heteroscedastic regression

This article considers REML (residual or restricted maximum likelihood) estimation for heteroscedastic linear models. An explicit algorithm is given for REML scoring which yields the REML estimates together with their standard errors and likelihood values. The algorithm includes a Levenberg-Marquardt restricted step modification that ensures that the REML likelihood increases at each iteration. This article shows how the complete computation, including the REML information matrix, may be carried out in O(n) operations.