Robust predictive distribution and bias-calibration in Linear Models

Abstract

This thesis focuses on the concept of predictive distributions and bias calibration. At first, an extension of the concept of predictive distributions under contamination is studied in the case of Generalized Linear Models. A sensitivity analysis of the impact of contamination on the predictive distribution is studied making use of the class of $M$-estimators. In a second step, based on the available literature on bias-calibrated estimation in linear regression, the bases to implement bias-calibration for predictive distributions are studied and developed. This development is based on the finite-sample setting and an important aspect of the reasoning behind this contribution is the distinction between representative and non-representative outliers. As a result of this distinction, the use of the bias-calibration approach allows to integrate information from representative outliers within the predictive distribution.