Conditional transformation models

Torsten Hothorn

doi:10.1111/rssb.12017

Return

Conditional transformation models

2013-03-20

Torsten Hothorn *

Thomas Kneib

Buehlmann, Peter

DOI：10.1111/rssb.12017

Original

Save

View PDF

Abstract

En 中文

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.

Keywords:

Boosting

Conditional distribution function

Conditional quantile function

Continuous ranked probability score

Prediction intervals

Structured additive regression

AI Summary

Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.