ABSTRACT
The two basic algorithms for fitting the parametric model with respect to β, and the nonparametric model with respect to β and γ for fixed λ, are the RS and the CG algorithms. The RS algorithm, which is a generalization of the algorithm, used by R. A. Rigby and D. M. Stasinopoulos for fitting mean and dispersion additive models. This algorithm does not use the cross derivatives of the log-likelihood. The CG algorithm is rather unstable, especially at the beginning of the iterations, and diverges easily. The RS algorithm is generally far more stable and in most cases faster, so it is used as the default. The idea of the local scoring algorithm is repeated weighted fits to a modified response variable, using modified weights, until convergence of the global deviance. Estimation of the beta and gamma parameters is done within the modified backfitting part of the algorithm. The backfitting algorithm is a version of the Gauss—Seidel algorithm.
