Forecasting aggregation methods are widely used in fields like economics, climate science, and machine learning to combine multiple predictions for better accuracy. While the Neyman aggregator—a theoretically grounded method for adversarial settings—offers a solid foundation, it has limitations. It optimizes for quadratic loss (less common in forecasting) and restricts aggregators to linear combinations, potentially missing higher-order patterns in real-world data.

Improving the Neyman Aggregator

One way to enhance this method could involve two key adjustments:

• Switching to log loss, which is more aligned with probabilistic forecasting tasks like weather or financial predictions, as it penalizes overconfidence more sharply.
• Expanding beyond linear combinations to include non-linear terms (e.g., squared predictions or interactions), allowing the aggregator to model complex relationships between forecasts.

This would require reformulating the theoretical framework, possibly using adversarial game theory or robust optimization techniques, followed by empirical testing against benchmarks like the M4 competition dataset.

Potential Applications and Advantages

Such an improved aggregator could benefit:

• Researchers developing robust forecasting methods.
• Practitioners in economics or meteorology who rely on aggregated predictions.
• Prediction platforms (e.g., Metaculus) seeking more accurate combined forecasts.

Compared to existing methods like Bayesian averaging or simple mean aggregation, this approach might offer better robustness in adversarial settings (e.g., prediction markets) and improved accuracy when forecasts exhibit non-linear dependencies.

Execution and Validation

A step-by-step approach could start with a simpler version—perhaps just switching to log loss while keeping linear aggregation—to isolate the impact of each change. Later phases could introduce non-linear terms and test performance under adversarial conditions, such as biased or manipulated forecasts. Computational challenges might arise, but approximations or restricted non-linear functions could help balance accuracy and efficiency.

If successful, this refined aggregator could fill a gap in robust forecasting, offering a method that’s both theoretically sound and practically adaptable.