1,721,191 research outputs found
Multivariate Conditional Transformation Models
Full text linkRegression models describing the joint distribution of multivariate response
variables conditional on covariate information have become an important aspect
of contemporary regression analysis. However, a limitation of such models is
that they often rely on rather simplistic assumptions, e.g. a constant
dependency structure that is not allowed to vary with the covariates or the
restriction to linear dependence between the responses only. We propose a
general framework for multivariate conditional transformation models that
overcomes these limitations and describes the entire distribution in a
tractable and interpretable yet flexible way conditional on nonlinear effects
of covariates. The framework can be embedded into likelihood-based inference,
including results on asymptotic normality, and allows the dependence structure
to vary with covariates. In addition, the framework scales well beyond
bivariate response situations, which were the main focus of most earlier
investigations. We illustrate the application of multivariate conditional
transformation models in a trivariate analysis of childhood undernutrition and
demonstrate empirically that our approach can be beneficial compared to
existing benchmarks such that complex truly multivariate data-generating
processes can be inferred from observations
Probabilistic Time Series Forecasts with Autoregressive Transformation Models
Full text linkProbabilistic forecasting of time series is an important matter in many
applications and research fields. In order to draw conclusions from a
probabilistic forecast, we must ensure that the model class used to approximate
the true forecasting distribution is expressive enough. Yet, characteristics of
the model itself, such as its uncertainty or its feature-outcome relationship
are not of lesser importance. This paper proposes Autoregressive Transformation
Models (ATMs), a model class inspired by various research directions to unite
expressive distributional forecasts using a semi-parametric distribution
assumption with an interpretable model specification. We demonstrate the
properties of ATMs both theoretically and through empirical evaluation on
several simulated and real-world forecasting datasets
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