Proper Calibeating
Dean P. Foster and Sergiu Hart
Abstract
The classic concept of "calibrated
forecasts," and its more recent refinement of
"calibeating," are defined with respect
to the standard quadratic scoring rule. We extend these notions to the class
of proper scoring rules (for which the best forecast is the true
distribution), and define proper calibration and proper
calibeating by requiring the errors to
converge to zero uniformly over all
proper Lipschitz scoring rules. We first establish that calibration always
implies proper calibration, whereas calibeating need not imply proper
calibeating. Second, we show how to guarantee proper calibeating, as well as
continuous proper calibeating by a deterministic
procedure, and proper multicalibeating.
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First version: December 2025
Last modified:
© Sergiu Hart