In prediction-powered inference, predictions supplement labeled outcomes to improve estimation. We combine a prediction-corrected score and an auxiliary moment in a generalized method of moments (GMM) criterion. The resulting estimator is first-order equivalent to the corresponding corrected-score root under regularity conditions, but the auxiliary penalty can change the finite-sample fit. In a multiparameter Gaussian linear model with low noise, retaining this penalty reduces risk relative to bounded scalar corrected-score roots. We then introduce covariance-calibrated prediction-powered inference (CC-PPI), which uses prediction scores from both samples to reweight the penalty. With a spectrally protected half-strength update, CC-PPI retains regular first-order efficiency and strictly reduces risk relative to uncalibrated full GMM in a Gaussian linear low-noise regime that tolerates some prediction error and in a structured multiparameter logistic model conditional on the existence of a finite pilot estimate. Targeted simulations isolate the gains from calibration and show that they can reverse as prediction error grows. Broader simulations and four applications evaluate point estimation and the coverage and width of full-refit bootstrap intervals for linear projections.

翻译：暂无翻译