
Open access
Author
Hothorn, Torsten
Möst Lisa
Buehlmann, Peter
Date
2018-03Type
- Journal Article
Abstract
We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterization of the uncon- ditional 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 frame- work 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 con- tinuous 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. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000204802Publication status
publishedJournal / series
Scandinavian Journal of StatisticsVolume
Pages / Article No.
Publisher
Wiley-BlackwellSubject
Censoring; conditional distribution function; Conditional quantile function; distribution regression; transformation mode; truncationOrganisational unit
02537 - Seminar für Statistik (SfS) / Seminar for Statistics (SfS)03502 - Bühlmann, Peter L. / Bühlmann, Peter L.
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