Proper Calibeating (opens in new tab)

The classic concept of "calibrated forecasts" and its more recent refinement, "calibeating," are defined with respect to the standard quadratic scoring rule. We extend these notions to the class of $\textit{proper}$ scoring rules (for which the best forecast is the true distribution) and define $\textit{proper-calibration}$ and $\textit{proper-calibeating}$ by requiring the errors to converge to zero uniformly over all bounded proper scoring r...