Adaptive linear models for regression

The general setting of regression analysis is to identify a relationship between a response variable Y and one or several explanatory variables X by using a learning sample. In a prediction framework, the main assumption for predicting Y on a new sample of X observations is that the regression model Y = f(X) + ǫ is still valid. Unfortunately, this assumption is not always true in practice and the model could have changed. We therefore propose to adapt the original regression model to a new sample by estimating a transformation between the original regression function f(X) and the new one f∗(X). The main interest of this work is that a model for the new population can be build with only few observations. The efficiency of this strategy is illustrated by applications on artificial and real datasets, including the modelling of the housing market in different U.S. cities in which the regression model of a reference city is adapted to another city. A package for the R software dedicated to adaptive linear models is available on the author’s webpage.