Resumen de Density-on-scalar regression models with an application in gender economics

Eva-Maria Maier, Almond Stöcker, Bernd Fitzenberger, Sonja Greven

• We provide a gradient boosting approach to estimate functional additive regression models with probability density functions as response variables and scalar covariates. To respect the special properties of densities, we formulate the regression model in a Bayes Hilbert space. This allows for a variety of applications, in particular for mixed densities, which have positive probability masses at some points of an interval. We illustrate how to handle this challenge by means of a motivating data set from the German Socio-Economic Panel Study (SOEP). In this application, we analyze the distribution of the woman's share in a couple's total labor income, which has positive probability masses at zero and one, using covariate e ects for year, federal state, and age of the youngest child.