Most Likely Transformations

Abstract

We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation 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 parameterisation 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 allowing the same flexibility as the theory developed here was employed to illustrate the wide range of possible applications.

Accepted for publication by the Scandinavian Journal of Statistics 2017-06-19

References in corpus (1)

• Estimation of a semiparametric transformation model

Cited by in corpus (20)

• A review of predictive uncertainty estimation with machine learning
• Short-Term Density Forecasting of Low-Voltage Load using Bernstein-Polynomial Normalizing Flows
• Bayesian Inference for Regression Copulas
• Survival Forests under Test: Impact of the Proportional Hazards Assumption on Prognostic and Predictive Forests for ALS Survival
• Distribution-Free Location-Scale Regression
• Transformation Forests
• Top-down Transformation Choice
• Deep transformation models for functional outcome prediction after acute ischemic stroke
• Distributional Anchor Regression
• Multivariate Conditional Transformation Models
• Robust multiple comparisons against a control group with application in toxicology
• What Makes Forest-Based Heterogeneous Treatment Effect Estimators Work?
• Model-based causal feature selection for general response types
• Deep Conditional Transformation Models
• Flexible Predictive Distributions from Varying-Thresholds Modelling
• Asymptotically Exact and Fast Gaussian Copula Models for Imputation of Mixed Data Types
• Claiming trend in toxicological and pharmacological dose-response studies: an overview on statistical methods and related R-Software
• Transformation Models for Flexible Posteriors in Variational Bayes
• Approximation Methods for Mixed Models with Probit Link Functions
• Simultaneous comparisons of treatments versus control (Dunnett-type tests) for location-scale alternatives