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Title: Additive density-on-scalar regression in Bayes Hilbert spaces with an application to gender economics Authors:  Eva-Maria Maier - Humboldt University of Berlin (Germany) [presenting]
Sonja Greven - Humboldt University of Berlin (Germany)
Almond Stoecker - Humboldt University of Berlin (Germany)
Bernd Fitzenberger - Institute for Employment Research (Germany)
Abstract: Functional additive regression models are presented for probability density functions as responses with scalar covariates. To respect the special properties of densities, i.e., nonnegativity and integration to one, we formulate the model for densities in a Bayes Hilbert space with respect to an arbitrary finite measure. Besides continuous and discrete densities, this also allows for, e.g., mixed densities, having discrete point masses at some points of an interval. For estimation, we propose a gradient boosting algorithm, which allows for potentially numerous flexible covariate effects and model selection. We apply our approach to a motivating data set from the German Socio-Economic Panel Study (SOEP) on the distribution of the woman's share in a couple's total labor income - an example for mixed densities since the woman's income share is a continuous variable having discrete point masses at zero and one for single-earner couples. Our approach assumes the response densities are observed directly. If we have individual-level data, we can apply our approach to estimated densities. Alternatively, we currently work on an approach to model the conditional densities directly from individual observations, which we will sketch in an outlook.