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Osband's principle for identification functions.

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Summary
This summary is machine-generated.

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.

Keywords:
CalibrationCharacterisationIdentification functionPoint forecastsZ-estimation

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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.