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We provide a review on the "optimal fingerprinting" approach as summarized inAllen and Tett (1999) from a point view of statistical inference in light ofthe recent criticism of McKitrick (2021). Our review finds that the "optimalfingerprinting" approach would survive much of McKitrick (2021)'s criticismunder two conditions: (i) the null simulation of the climate model isindependent of the physical observations and (ii) the null simulation providesconsistent estimation of the residual covariance matrix of the physicalobservations, both depend on the conduction and the quality of the climatemodels. If the latter condition fails, the estimator would be still unbiasedand consistent under routine conditions, but losing the "optimal" aspect of theapproach. The residual consistency test suggested by Allen and Tett (1999) isvalid for checking the agreement between the residual covariances of the nullsimulation and the physical observations. We further outline the connectionbetween the "optimal fingerprinting" approach and the Feasible GeneralizedLeast Square.

A Review on the Optimal Fingerprinting Approach in Climate Change Studies