Abstract
In this chapter, we define optimality and robustness under distortions for statistical forecasting. The problem of statistical forecasting is stated in the most general form and then specialized for point or interval forecasting and different levels of prior uncertainty. The chapter introduces performance characteristics of forecasting statistics based on loss functions and risk functionals. In order to define mathematically rigorous robustness characteristics, a classification of the types of distortions common to applications is made, and the relevant mathematical distortion models are constructed. Robustness of statistical forecasting techniques is defined in terms of the following robustness characteristics: the guaranteed (upper) risk, the risk instability coefficient, the δ-admissible distortion level.
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Kharin, Y. (2013). Performance and Robustness Characteristics in Statistical Forecasting. In: Robustness in Statistical Forecasting. Springer, Cham. https://doi.org/10.1007/978-3-319-00840-0_4
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DOI: https://doi.org/10.1007/978-3-319-00840-0_4
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