Rage Against the Mean – A Review of Distributional Regression Approaches

Kneib, Thomas; Silbersdorff, Alexander; Säfken, Benjamin

doi:10.1016/j.ecosta.2021.07.006

Cited by 46 publications

(27 citation statements)

References 84 publications

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“…The Weibull distributional regression (WDR), an example of parametric distributional regression (Kneib et al, 2021) with the Weibull conditional distribution assumption, is another method we used for estimating directional wind speed quantiles. Under Weibull distribution assumptions, we need to estimate how the scale λ and shape κ parameters vary as functions of wind direction x with periodicity constraints.…”

Section: Weibull Distributional Regressionmentioning

confidence: 99%

“…Specifically, we model wind direction using von Mises mixture distributions (Mardia and Sutton, 1975), a mixture model of the von Mises distribution (Mardia, 1975) to preserve the circular nature. We then explore two distributional regression (see Kneib et al, 2021, for a review) approaches, namely Weibull regression to accommodate the right skewness of wind speed distributions (Brown et al, 1984;Monahan, 2006;Solari and Losada, 2016) and quantile regression (Koenker and Bassett Jr, 1978, see Sec. 3 for more details) to estimate the conditional distribution of wind speed given the wind direction (directional wind speed distribution hereafter). Combining the estimated wind direction distribution [Φ] and the estimated directional wind speed distribution [ρ|Φ = φ] allows one to capture the joint distribution of wind speed and direction [ρ, Φ] and hence their interactions.…”

Section: Introductionmentioning

confidence: 99%

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Station-wise statistical joint assessment of wind speed and direction under future climates across the United States

Wu¹,

Bessac²,

Huang³

et al. 2022

Preprint

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This study develops a statistical conditional approach to evaluate climate model performance in wind speed and direction and to project their future changes under the representative concentration pathway (RCP) 8.5 scenario over inland and offshore locations across the Continental United States (CONUS). The proposed conditional approach extends the scope of existing studies by characterizing the changes of the full range of the joint wind speed and direction distribution. A von Mises mixture distribution is used to model wind directions across models and climate conditions. Directional wind speed distributions are estimated using two statistical methods: a Weibull distributional regression model and a quantile regression model, both of which enforce the circular constraint to their resulting estimates of directional distributions. Projected uncertainties associated with different climate models and model internal variability are investigated and compared with the climate change signal to quantify the statistical significance of the future projections. In particular, this work extends the concept of internal variability to the standard deviation and high quantiles to assess the relative magnitudes to their projected changes. The evaluation results show that the studied climate model capture both historical wind speed, wind direction, and their dependencies reasonably well over both inland and offshore locations. In the future, most of the locations show no significant changes in mean wind speeds in both winter and summer, although the changes in standard deviation and 95thquantile show some robust changes over certain locations in winter. However, in winter, high directional wind speeds are projected to decrease in Northwest, Colorado and Northern Great Plains. In summer, directional high wind speeds over southern Great Plains slightly increase while high directional wind speeds over offshore locations do not change in future. The proposed conditional approach enables the characterization of the directional wind speed distributions, which offers additional insights for the joint assessment of speed and direction.

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Section: Weibull Distributional Regressionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Station-wise statistical joint assessment of wind speed and direction under future climates across the United States

Wu¹,

Bessac²,

Huang³

et al. 2022

Preprint

View full text Add to dashboard Cite

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“…Here we use a subset of the dataset that includes up to 87 days of sensing and that was collected during a study period from October 28th, 2017 to January 22nd, 2018. After pre-processing, we obtain activities from 342 participants in Germany in 6-hour windows ([0-6], [6][7][8][9][10][11][12], [12][13][14][15][16][17][18], [18][19][20][21][22][23][24]) throughout each day of the study period.…”

Section: D2 Data Set and Model Specificationmentioning

confidence: 99%

“…. , K [32,22]. An interesting property to investigate in future research is how DR can account for aleatoric uncertainty.…”

Section: F Outlook: Distributional Regressionmentioning

confidence: 99%

Factorized Structured Regression for Large-Scale Varying Coefficient Models

Rügamer¹,

Bender²,

Wiegrebe³

et al. 2022

Preprint

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Recommender Systems (RS) pervade many aspects of our everyday digital life. Proposed to work at scale, state-of-the-art RS allow the modeling of thousands of interactions and facilitate highly individualized recommendations. Conceptually, many RS can be viewed as instances of statistical regression models that incorporate complex feature effects and potentially non-Gaussian outcomes. Such structured regression models, including time-aware varying coefficients models, are, however, limited in their applicability to categorical effects and inclusion of a large number of interactions. Here, we propose Factorized Structured Regression (FaStR) for scalable varying coefficient models. FaStR overcomes limitations of general regression models for large-scale data by combining structured additive regression and factorization approaches in a neural network-based model implementation. This fusion provides a scalable framework for the estimation of statistical models in previously infeasible data settings. Empirical results confirm that the estimation of varying coefficients of our approach is on par with state-of-the-art regression techniques, while scaling notably better and also being competitive with other time-aware RS in terms of prediction performance. We illustrate FaStR's performance and interpretability on a large-scale behavioral study with smartphone user data.

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“…The implicit copula here is a "regression copula" process with respect to the covariates as in Klein and Smith (2019). The copula model forms a distributional regression (Klein et al, 2015;Kneib et al, 2021), where the five factors affect the entire distribution of equity returns, not just its first or other moments. In both applications the implicit copulas are of dimension equal to the number of observations, so that they are high-dimensional.…”

Section: Introductionmentioning

confidence: 99%

Implicit Copulas: An Overview

Smith¹

2021

Preprint

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Implicit copulas are the most common copula choice for modeling dependence in high dimensions. This broad class of copulas is introduced and surveyed, including elliptical copulas, skew t copulas, factor copulas, time series copulas and regression copulas. The common auxiliary representation of implicit copulas is outlined, and how this makes them both scalable and tractable for statistical modeling. Issues such as parameter identification, extended likelihoods for discrete or mixed data, parsimony in high dimensions, and simulation from the copula model are considered. Bayesian approaches to estimate the copula parameters, and predict from an implicit copula model, are outlined. Particular attention is given to implicit copula processes constructed from time series and regression models, which is at the forefront of current research. Two econometric applications-one from macroeconomic time series and the other from financial asset pricing-illustrate the advantages of implicit copula models.

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Rage Against the Mean – A Review of Distributional Regression Approaches

Cited by 46 publications

References 84 publications

Station-wise statistical joint assessment of wind speed and direction under future climates across the United States

Station-wise statistical joint assessment of wind speed and direction under future climates across the United States

Factorized Structured Regression for Large-Scale Varying Coefficient Models

Implicit Copulas: An Overview

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