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Conditional transformation models


  • Torsten Hothorn
  • Thomas Kneib
  • Peter Bühlmann


type="main" xml:id="rssb12017-abs-0001"> The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models estimate only the conditional mean as a function of the explanatory variables and assume that higher moments are not affected by the regressors. The underlying reason for such a restriction is the assumption of additivity of signal and noise. We propose to relax this common assumption in the framework of transformation models. The novel class of semiparametric regression models proposed herein allows transformation functions to depend on explanatory variables. These transformation functions are estimated by regularized optimization of scoring rules for probabilistic forecasts, e.g. the continuous ranked probability score. The corresponding estimated conditional distribution functions are consistent. Conditional transformation models are potentially useful for describing possible heteroscedasticity, comparing spatially varying distributions, identifying extreme events, deriving prediction intervals and selecting variables beyond mean regression effects. An empirical investigation based on a heteroscedastic varying-coefficient simulation model demonstrates that semiparametric estimation of conditional distribution functions can be more beneficial than kernel-based non-parametric approaches or parametric generalized additive models for location, scale and shape.

Suggested Citation

  • Torsten Hothorn & Thomas Kneib & Peter Bühlmann, 2014. "Conditional transformation models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 3-27, January.
  • Handle: RePEc:bla:jorssb:v:76:y:2014:i:1:p:3-27

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    Cited by:

    1. Samantha Leorato & Franco Peracchi, 2015. "Comparing Distribution and Quantile Regression," EIEF Working Papers Series 1511, Einaudi Institute for Economics and Finance (EIEF), revised Oct 2015.
    2. Möst Lisa & Hothorn Torsten, 2015. "Conditional Transformation Models for Survivor Function Estimation," The International Journal of Biostatistics, De Gruyter, vol. 11(1), pages 23-50, May.
    3. Stanislav Anatolyev & Jozef Barunik, 2017. "Forecasting dynamic return distributions based on ordered binary choice and cross-quantile predictability connection," Papers 1711.05681,, revised Oct 2018.
    4. Souhaib Ben Taieb & James W. Taylor & Rob J. Hyndman, 2017. "Coherent Probabilistic Forecasts for Hierarchical Time Series," Monash Econometrics and Business Statistics Working Papers 3/17, Monash University, Department of Econometrics and Business Statistics.
    5. Alexander Silbersdorff & Julia Lynch & Stephan Klasen & Thomas Kneib, 2017. "Reconsidering the Income-Illness Relationship Using Distributional Regression: An Application to Germany," SOEPpapers on Multidisciplinary Panel Data Research 931, DIW Berlin, The German Socio-Economic Panel (SOEP).

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