Point forecasting and forecast evaluation with generalized Huber loss

@article{Taggart2021PointFA,
  title={Point forecasting and forecast evaluation with generalized Huber loss},
  author={Robert J. Taggart},
  journal={Electronic Journal of Statistics},
  year={2021}
}
: Huber loss, its asymmetric variants and their associated func- tionals (here named Huber functionals ) are studied in the context of point forecasting and forecast evaluation. The Huber functional of a distribution is the set of minimizers of the expected (asymmetric) Huber loss, is an intermediary between a quantile and corresponding expectile, and also arises in M-estimation. Each Huber functional is elicitable, generating the precise set of minimizers of an expected score, subject to weak… 
View PDF on arXiv
5 Citations
Highly Influential Citations
1
Background Citations
4
Methods Citations
2

Figures and Tables from this paper

5 Citations

Evaluation of point forecasts for extreme events using consistent scoring functions

We present a method for comparing point forecasts in a region of interest, such as the tails or centre of a variable's range. This method cannot be hedged, in contrast to selecting events…

Regression Diagnostics meets Forecast Evaluation: Conditional Calibration, Reliability Diagrams, and Coefficient of Determination

Model diagnostics and forecast evaluation are two sides of the same coin. A common principle is that fitted or predicted distributions ought to be calibrated or reliable, ideally in the sense of…

A review of probabilistic forecasting and prediction with machine learning

The topic of predictive uncertainty estimation with machine learning algorithms, as well as the related metrics (consistent scoring functions and proper scoring rules) for assessing probabilistic predictions are reviewed, sparking understanding on how to develop new algorithms tailored to users’ needs.

A scoring framework for tiered warnings and multicategorical forecasts based on fixed risk measures

The use of tiered warnings and multicategorical forecasts are ubiquitous in meteorological operations. Here, a flexible family of scoring functions is presented for evaluating the performance of…

Robust learning of Huber loss under weak conditional moment

References

SHOWING 1-10 OF 35 REFERENCES

Of quantiles and expectiles: consistent scoring functions, Choquet representations and forecast rankings

In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional. For example, forecasters might be asked to report the mean or a…

Quantiles as optimal point forecasts

Comparing Possibly Misspecified Forecasts

Abstract Recent work has emphasized the importance of evaluating estimates of a statistical functional (such as a conditional mean, quantile, or distribution) using a loss function that is consistent…

Making and Evaluating Point Forecasts

Typically, point forecasting methods are compared and assessed by means of an error measure or scoring function, with the absolute error and the squared error being key examples. The individual…

Evaluation of point forecasts for extreme events using consistent scoring functions

We present a method for comparing point forecasts in a region of interest, such as the tails or centre of a variable's range. This method cannot be hedged, in contrast to selecting events…

Risk management with expectiles

Expectiles (EVaR) are a one-parameter family of coherent risk measures that have been recently suggested as an alternative to quantiles (VaR) and to expected shortfall (ES). In this work we review…

Generalized Quantiles as Risk Measures

In the statistical and actuarial literature several generalizations of quantiles have been considered, by means of the minimization of a suitable asymmetric loss function. All these generalized…

Elicitability and its Application in Risk Management

Elicitability is a property of $\mathbb{R}^k$-valued functionals defined on a set of distribution functions. These functionals represent statistical properties of a distribution, for instance its…

Building cost functions minimizing to some summary statistics

  • Marco Saerens
  • Mathematics
    IEEE Trans. Neural Networks Learn. Syst.
  • 2000
The calculus of variations is used to derive necessary and sufficient conditions on the cost function ensuring that the output of the trained model approximates the conditional expectation of the desired output given the explanatory variables.

Robust estimation and shrinkage in ultrahigh dimensional expectile regression with heavy tails and variance heterogeneity

The asymmetric square loss and huber-type robust technique is combined to develop the robust expectile regression for ultrahigh dimensional heavy-tailed heterogeneous data and an efficient first-order optimization algorithm after locally linear approximation of the non-convex problem is proposed.