Flexible density regression methods

灵活的密度回归方法

• 批准号: 513634041
• 负责人: Professorin Dr. Sonja Greven
• 金额: --
• 依托单位: Lehrstuhl für Statistik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/513634041?language=en
• 关键词: Flexible; density; regression; methods

The goal of this project is to develop a unified framework of flexible semiparametric regression methods for densities to better describe and understand relationships between variables of interest. While limitations in traditional mean-oriented parametric modeling of (scalar) data have promoted a variety of extensions to other distributional characteristics (quantiles) or multiple distributional parameters (distributional regression), first methods have recently been developed in functional and compositional data analysis for probability densities as objects of statistical analysis. However, these branches of regression with flexible distributions (individual-level approaches) and statistical analysis of distributions (density-level approaches) have so far been independently developed. Our mission is to join them for fruitful mutual enrichment, facilitating methodological developments. To illustrate the demand of flexible density regression methods, we refer to an example from gender economics: the distribution of the woman's share of a couple's labor income is important for questions on gender identity norms. As a probability distribution, it presents a mixed distribution on [0,1] with positive probability mass at 0 and 1 (for single-income couples) and a continuous - often bimodal - density in between (for double-income couples). It is then of interest to relate this distribution to variables that may influence the distribution such as (age of) children in the household, year or living region. Clear differences occur, for instance, between the eastern and western states in Germany. The density is particularly of interest, as it makes shifts in probability mass or bimodalities due to subgroups easily visible, and as it extends well to discrete, continuous, mixed or bivariate distributions. Such analyses require methods that can model the whole distribution flexibly depending on covariates without parametric assumptions such as normality, and that allow for linear, nonlinear and random effects. We will address this by developing suitable methods for density regression. Depending on the data situation, density regression methods are required and will be developed for density-valued data - e.g. when a histogram is provided for administrative data or is used to summarize massive data - as well as for individual scalar data, when interest lies in modeling the conditional density given covariates. In our unified approach, these two scenarios present two sides of the same coin instead of referring to two different branches of statistics. We will develop methods for continuous densities (e.g. income), discrete densities, i.e. compositional data (e.g. time use over discrete categories), as well as mixed densities (e.g. a woman's fraction of household labor income). Additionally, we will extend this to bivariate densities e.g. when jointly looking at a couple within a household, allowing to overcome also restrictive correlation assumptions.

该项目的目标是为密度开发一个灵活的半参数回归方法的统一框架，以更好地描述和理解感兴趣的变量之间的关系。虽然传统的（标量）数据的面向均值的参数化建模的局限性促进了对其他分布特征（分位数）或多个分布参数（分布回归）的各种扩展，但最近在概率密度作为统计分析对象的功能和组成数据分析中开发了第一种方法。然而，这些具有灵活分布的回归分支（个体水平方法）和分布的统计分析（密度水平方法）迄今为止都是独立发展的。我们的使命是与他们一起富有成效地相互充实，促进方法论的发展。为了说明灵活密度回归方法的必要性，我们引用了性别经济学中的一个例子：女性在夫妻劳动收入中所占份额的分布对性别认同规范的问题很重要。作为一个概率分布，它在[0,1]上呈现一个混合分布，在0和1处的概率质量为正（对于单收入夫妇），在两者之间呈现连续的（通常是双峰的）密度（对于双收入夫妇）。因此，将这种分布与可能影响分布的变量（如家庭中儿童的年龄、年份或居住地区）联系起来是有意义的。例如，德国的东部和西部各州之间就存在明显的差异。密度是特别有趣的，因为它使得由于子群而引起的概率质量或双模态的变化很容易看到，并且因为它很好地扩展到离散、连续、混合或二元分布。这种分析需要能够灵活地根据协变量对整个分布建模的方法，而不需要参数假设（如正态性），并且允许线性、非线性和随机效应。我们将通过开发合适的密度回归方法来解决这个问题。根据数据的情况，密度回归方法是必需的，并且将被开发用于密度值数据——例如，当为管理数据提供直方图或用于汇总大量数据时——以及单个标量数据，当兴趣在于对给定协变量的条件密度建模时。在我们的统一方法中，这两种情况呈现了同一枚硬币的两面，而不是指两个不同的统计分支。我们将开发连续密度（如收入）、离散密度(即组成数据（如离散类别的时间使用）以及混合密度（如女性在家庭劳动收入中所占比例）的方法。此外，我们将把它扩展到双变量密度，例如，当共同观察一个家庭中的一对夫妇时，允许克服限制性的相关性假设。