arXiv 12 Dec 2024 · Econometrics
arXiv:2412.09430 · PDF · DOI · OpenAlex · Extracted main text
The variance of a linearly combined forecast distribution (or linear pool) consists of two components: The average variance of the component distributions (`average uncertainty'), and the average squared difference between the components' means and the pool's mean (`disagreement'). This paper shows that similar decompositions hold for a class of uncertainty measures that can be constructed as entropy functions of kernel scores. The latter are a rich family of scoring rules that covers point and distribution forecasts for univariate and multivariate, discrete and continuous settings. We further show that the disagreement term is useful for understanding the ex-post performance of the linear pool (as compared to the component distributions), and motivates using the linear pool instead of other forecast combination techniques. From a practical perspective, the results in this paper suggest principled measures of forecast disagreement in a wide range of applied settings.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Allen, S., Ginsbourger, D., and Ziegel, J (2025) Efficient pooling of predictions via kernel embeddings | 0.950 | 7 | 6 | 86% |
| 2 | Neyman, E. and Roughgarden, T (2023) From proper scoring rules to max-min optimal forecast aggregation | 0.874 | 6 | 2 | 100% |
| 3 | Gneiting, T. and Ranjan, R (2013) Combining predictive distributions | 0.874 | 5 | 2 | 100% |
| 4 | Knüppel, M., Krüger, F., and Pohle, M.-O (2022) Score-based calibration testing for multivariate forecast distributions | 0.843 | 4 | 3 | 75% |
| 5 | Lichtendahl Jr, K. C., Grushka-Cockayne, Y., and Winkler, R. L (2013) Is it better to average probabilities or quantiles? | 0.830 | 7 | 4 | 57% |
| 6 | Gneiting, T. and Raftery, A. E (2007) Strictly proper scoring rules, prediction, and estimation | 0.822 | 9 | 5 | 56% |
| 7 | Thorarinsdottir, T. L., Gneiting, T., and Gissibl, N (2013) Using proper divergence functions to evaluate climate models | 0.737 | 3 | 3 | 67% |
| 8 | Elliott, G. and Liao, J (2025) Combining forecasts-on why averaging beats optimal linear weights | 0.737 | 3 | 2 | 100% |
| 9 | Gneiting, T (2012) On the cover-hart inequality: What's a sample of size one worth? | 0.693 | 6 | 2 | 50% |
| 10 | Clark, T. E. and Mertens, E (2024) Survey expectations and forecast uncertainty | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 78 scored citations.