Conditional transformation models
Conditional transformation models
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DOI：
10.1111/rssb.12017
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发表时间：
2014-01-01
影响因子：
5.8
通讯作者：
Buehlmann, Peter
中科院分区：
文献类型：
--
作者：
Hothorn, Torsten;Kneib, Thomas;Buehlmann, Peter
回归分析的最终目标是获得有关给定一组解释变量的响应条件分布的信息。然而，这个目标很少实现，因为大多数已建立的回归模型仅估计条件均值作为解释变量的函数，并假设更高的矩不受回归量的影响。这种限制的根本原因是信号和噪声的可加性假设。我们建议在转换模型的框架中放宽这一常见假设。本文提出的新型半参数回归模型允许变换函数依赖于解释变量。这些变换函数是通过概率预测的评分规则的正则优化来估计的，例如连续排名的概率得分。相应的估计条件分布函数是一致的。条件变换模型对于描述可能的异方差性、比较空间变化的分布、识别极端事件、推导预测区间以及选择均值回归效应之外的变量可能有用。基于异方差变系数模拟模型的实证研究表明，条件分布函数的半参数估计比基于核的非参数方法或位置、尺度和形状的参数广义加性模型更有利。
The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models estimate only the conditional mean as a function of the explanatory variables and assume that higher moments are not affected by the regressors. The underlying reason for such a restriction is the assumption of additivity of signal and noise. We propose to relax this common assumption in the framework of transformation models. The novel class of semiparametric regression models proposed herein allows transformation functions to depend on explanatory variables. These transformation functions are estimated by regularized optimization of scoring rules for probabilistic forecasts, e.g. the continuous ranked probability score. The corresponding estimated conditional distribution functions are consistent. Conditional transformation models are potentially useful for describing possible heteroscedasticity, comparing spatially varying distributions, identifying extreme events, deriving prediction intervals and selecting variables beyond mean regression effects. An empirical investigation based on a heteroscedastic varying-coefficient simulation model demonstrates that semiparametric estimation of conditional distribution functions can be more beneficial than kernel-based non-parametric approaches or parametric generalized additive models for location, scale and shape.