Rank-Based Estimation for Generalized Additive Models

Abstract

This thesis focuses on the improvement of generalized additive models (GAMs) using rank estimators. We introduce estimation of the smoothing functions in GAMs via backfitting in a local scoring algorithm using maximization of the expected log likelihood function with weights. Improvements of GAM estimation have focused on the smoothers used in the local scoring algorithm, but poor prediction for non-Gaussian data motivates the need for robust estimation of GAMs. Rank-based estimation as a robust and efficient alternative to the likelihood-based estimation of GAMs is proposed, and it is shown that rank GAM estimators can be restructured as iteratively reweighted GAM estimators. Simulations further support the use of rank-based GAM estimation for heavy-tailed or contaminated sources of data common in climate studies. Successful application of rank GAM estimation is employed for fisheries data, a field which commonly uses GAMs for their high degree of flexibility in modeling complex systems and could benefit from improved model prediction performance for non-Gaussian data. Cross-validation shows improved prediction performance for rank GAMs over GAMs, and improved adjusted R-squared values highlight the better fit of rank GAMs for the given data.