Most Likely Transformations
Most Likely Transformations
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DOI：
10.1111/sjos.12291
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发表时间：
2018-03-01
影响因子：
1
通讯作者：
Buehlmann, Peter
中科院分区：
文献类型：
--
作者：
Hothorn, Torsten;Moest, Lisa;Buehlmann, Peter
本文提出并研究了条件变换模型类中极大似然估计的性质。基于一个合适的显式参数化的无条件或有条件的转换函数，我们建立了一个级联的越来越复杂的转换模型，可以估计，比较和分析的最大似然框架。任何单变量响应变量的无条件或条件分布函数的模型可以在相同的理论和计算框架中简单地通过选择适当的变换函数及其参数化来建立和估计。直接评估分布函数的能力使我们能够基于精确的似然估计模型，特别是在存在随机截尾或截断的情况下。对于离散和连续响应，我们建立了所提出的估计量的渐近正态性。一个参考软件实现的最大似然为基础的估计条件变换模型，允许相同的灵活性，在这里开发的理论被用来说明广泛的可能的应用。
We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterization of the unconditional or conditional transformation function, we establish a cascade of increasingly complex transformation models that can be estimated, compared and analysed in the maximum likelihood framework. Models for the unconditional or conditional distribution function of any univariate response variable can be set up and estimated in the same theoretical and computational framework simply by choosing an appropriate transformation function and parameterization thereof. The ability to evaluate the distribution function directly allows us to estimate models based on the exact likelihood, especially in the presence of random censoring or truncation. For discrete and continuous responses, we establish the asymptotic normality of the proposed estimators. A reference software implementation of maximum likelihood-based estimation for conditional transformation models that allows the same flexibility as the theory developed here was employed to illustrate the wide range of possible applications.