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Osband's principle for identification functions
Timo Dimitriadis1,2, Tobias Fissler3,4, Johanna Ziegel5
1Alfred Weber Institute of Economics, Heidelberg University, Bergheimer Str. 58, 69115 Heidelberg, Germany.
Statistical Papers (Berlin, Germany)
|March 25, 2024
Summary
This study characterizes identification functions, crucial for statistical estimation and forecast validation. We define these functions, which are zero in expectation at the true value, for various statistical functionals.
Area of Science:
- Statistics
- Econometrics
- Machine Learning
Background:
- Identification functions are fundamental in statistical inference.
- They are essential for validating forecasts and dynamic models.
- Existing literature lacks a complete characterization for vector-valued functionals.
Purpose of the Study:
- To fully characterize the class of strict identification functions.
- To extend the understanding of identification functions to vector-valued functionals.
- To provide a rigorous framework for their application in statistical modeling.
Main Methods:
- Mathematical derivation and theoretical analysis.
- Exploration of properties under mild regularity conditions.
- Characterization of the space of identification functions.
Main Results:
- A complete characterization of strict identification functions is provided.
- The theory is extended to handle vector-valued statistical functionals.
- The derived class of functions satisfies key theoretical properties.
Conclusions:
- The study offers a comprehensive understanding of identification functions.
- This work facilitates advancements in statistical estimation and forecast validation.
- The findings are applicable to complex, vector-valued functional estimation problems.
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