标题： 加性密度回归 显示英文标题

标题： Additive Density Regression

摘要： 我们提出一种结构化的加性回归方法，以建模给定标量协变量的条件密度，其中仅观察到条件分布的样本。 这将我们的方法与标量数据的分布回归模型联系起来。 该模型在贝叶斯希尔伯特空间中表述——在求和和标量乘法下保持非负性和积分至一——相对于任意有限测度。 这使得可以考虑连续、离散和混合密度等。 我们的理论结果包括惩罚最大似然估计量的渐近存在性、唯一性、一致性以及渐近正态性，以及对（效应）密度的置信区域和推断。 对于估计，我们建议最大化对应于适当多项式或等价地泊松回归模型的惩罚对数似然，我们证明该模型可以逼近原始的惩罚最大似然问题。 我们将我们的框架应用于来自德国社会经济面板研究（SOEP）的一个有启发性的性别经济数据集，分析在年份、居住地和最小孩子的年龄协变量影响下，夫妻总劳动收入中女性份额的分布。 由于收入份额是一个连续变量，在单收入者夫妇中在零和一处具有离散点质量，相应的密度是混合类型。 显示英文摘要

摘要： We present a structured additive regression approach to model conditional densities given scalar covariates, where only samples of the conditional distributions are observed. This links our approach to distributional regression models for scalar data. The model is formulated in a Bayes Hilbert space -- preserving nonnegativity and integration to one under summation and scalar multiplication -- with respect to an arbitrary finite measure. This allows to consider, amongst others, continuous, discrete and mixed densities. Our theoretical results include asymptotic existence, uniqueness, consistency, and asymptotic normality of the penalized maximum likelihood estimator, as well as confidence regions and inference for the (effect) densities. For estimation, we propose to maximize the penalized log-likelihood corresponding to an appropriate multinomial, or equivalently, Poisson regression model, which we show to approximate the original penalized maximum likelihood problem. We apply our framework to a motivating gender economic data set from the German Socio-Economic Panel Study (SOEP), analyzing the distribution of the woman's share in a couple's total labor income given covariate effects for year, place of residence and age of the youngest child. As the income share is a continuous variable having discrete point masses at zero and one for single-earner couples, the corresponding densities are of mixed type.