Most Likely Transformations

Hothorn, Torsten; Möst, Lisa and Bühlmann, Peter (2018): Most Likely Transformations. In: Scandinavian Journal of Statistics, Vol. 45, No. 1: pp. 110-134

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 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Statistics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0303-6898
• Language: English