  We provide a review on the "optimal fingerprinting" approach as summarized in
Allen and Tett (1999) from a point view of statistical inference in light of
the recent criticism of McKitrick (2021). Our review finds that the "optimal
fingerprinting" approach would survive much of McKitrick (2021)'s criticism
under two conditions: (i) the null simulation of the climate model is
independent of the physical observations and (ii) the null simulation provides
consistent estimation of the residual covariance matrix of the physical
observations, both depend on the conduction and the quality of the climate
models. If the latter condition fails, the estimator would be still unbiased
and consistent under routine conditions, but losing the "optimal" aspect of the
approach. The residual consistency test suggested by Allen and Tett (1999) is
valid for checking the agreement between the residual covariances of the null
simulation and the physical observations. We further outline the connection
between the "optimal fingerprinting" approach and the Feasible Generalized
Least Square.
