Most Likely Transformations

By Torsten Hothorn, Lisa Möst, Peter Buhlmann. 2015

124 citations recorded by the source corpus.

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.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/62d2e3b89245668d37cdc851324f998465661595

Citations in the corpus

• Bernstein flows for flexible posteriors in variational Bayes (2022, unknown): “A large order M ensures an accurate approximation of the distribution, which is robust against a further increase of M (Hothorn et al. 2018; 1 3 Bernstein flows for flexible posteriors in variational Bayes Ramasinghe et al. 2021); this is also demonstrated in our experiments for the BBVI setting.”