A Minmax Regret Linear Regression Model Under Uncertainty in the Dependent Variable

This paper analyzes the simple linear regression model corresponding to a sample affected by errors from a non-probabilistic viewpoint. We consider the simplest case where the errors just affect the dependent variable and there only exists one explanatory variable. Moreover, we assume the errors affecting each observation can be bounded. In this context the minmax regret criterion is used in order to obtain a regression line with nearly optimal goodness of fit for any true values of the dependent variable. Theoretical results as well as numerical methods are stated in order to solve the optimization problem under different residual cost functions.