The comparison of different hypotheses, i.e. of competing models, is the basis of model specification. It may be performed along two main lines. The first one consists in associating with each model a loss function and in retaining the specification implying the smallest (estimated) loss. In...

This chapter discusses the formal and informal techniques that are commonly used to give quantitative answers in the field of distributional analysis. To this end, it covers subjects including inequality, poverty, and the modeling of income distributions. It also deals with parametric and...

We present a unifying view on various statistical estimation techniques including penalization, variational, and thresholding methods. These estimators are analyzed in the context of statistical linear inverse problems including nonparametric and change point regression, and high-dimensional...