Title: A general framework for prediction in multidimensional smoothing
Authors: Alba Carballo - Universidad Carlos III de Madrid (Spain) [presenting]
Maria Durban - Universidad Carlos II de Madrid (Spain)
Dae-Jin Lee - BCAM - Basque Center for Applied Mathematics (Spain)
Abstract: There are many situations in which prediction of new observations in the context of smoothing regression is needed (smooth time series, longitudinal models, etc.), but somehow this topic has been overlooked over the years. We propose a general framework for out-of-sample prediction in multidimensional smoothing. We explain how to construct basis and penalty matrices in a two-dimensional P-spline setting and show how prediction is carried out under different points of view: penalized regression, smooth mixed models and Gaussian process regression. We show the differences between the properties of the methodology used, and propose the use of constrained penalized splines to overcome the coherence problems that arise in the two dimensional case. One important application of the methods proposed is the forecasting of mortality rates from two-dimensional life's tables. We use data from the Human Mortality Data Base to illustrate our methodology.