Osband's Principle for Identification Functions

TL;DR

This paper characterizes the class of strict identification functions for statistical functionals like mean or median, which are crucial for forecast validation, estimation, and modeling, under mild regularity conditions.

Contribution

It provides a complete characterization of strict identification functions for possibly vector-valued functionals, advancing theoretical understanding.

Findings

Full characterization of identification functions for scalar and vector functionals

Applicable under mild regularity conditions

Enhances methods for forecast validation and statistical estimation

Abstract

Given a statistical functional of interest such as the mean or median, a (strict) identification function is zero in expectation at (and only at) the true functional value. Identification functions are key objects in forecast validation, statistical estimation and dynamic modelling. For a possibly vector-valued functional of interest, we fully characterise the class of (strict) identification functions subject to mild regularity conditions.