Adaptive linear models in regression for the modeling of housing market in different U.S. cities
Résumé
The general setting of regression analysis is to identify a relationship between a response variable $Y$ and one or several explanatory variables $\textbf{X}$ by using a learning sample. In a prediction framework, the main assumption for predicting $Y$ on a new sample of $\textbf{X}$ observations is that the regression model $Y=f(\textbf{X})+\epsilon$ is still valid. Unfortunately, this assumption is not always true in practice. We therefore propose to adapt the original regression model to the new sample by estimating a transformation between the original regression function $f(\textbf{X})$ and the new one $f^{*}(\textbf{X})$. The interest of this work is illustrated by an application to the modeling of housing market in different U.S. cities in which the regression model of a reference city is adapted to another city.